No, you can't cast a spell with your extra action from haste.
Despite including an attack as part of the cantrip, all cantrips use the Cast a Spell action, like any other spell. Haste's options are limited as you indicated, and Cast a Spell is not among the available options.
But... Divine Smite!
The paladin's Divine Smite feature is not a spell, despite being fueled by spell slots. Paladins have other kinds of smiting that are spells, but Divine Smite is not. It triggers when you hit a creature with a melee weapon attack, but does not take any sort of action; any melee weapon attack that hits will suffice.
Readying hasted Actions does not make haste overpowered
From your clarification in the comments, I will look at if doing so would make haste "very imbalanced and over powered".
In general
Rules-as-written, you can use your normal Action to Ready any available Action, while using one of the limited hasted Actions on your turn. With the proposed change, you could Dodge, Cast a Spell, or make a full set of Extra Attacks and still Ready a single attack.
Additionally, you could Ready two different Actions with two different triggers - one with your hasted Action and the other with your normal Action. When a trigger happens, you are explicitly allowed to ignore the trigger. "I Ready cure wounds to cast on the guy at my feet if he surrenders. I then use my hasted Action to Ready to attack the same guy if he instead fights back." You could only use your Reaction to respond to one of the triggers, but you could choose which one.
Dash and Disengage
Dash is useless to Ready. With your normal Action, you can Ready to move up to your speed, which is not the same as taking the Dash action. To make use of this, you would need some beneficial way to move outside of your turn without using your Reaction. Such an ability does not currently exist.
Similarly, Disengage is useless to Ready. It doesn't let you actually move; rather, it prevents opportunity attacks for the current turn.
Hide
If you find yourself in a bright room with a friendly Warlock, you could Ready a Hide action for when they cast darkness. Caveat: you can't move after this, so enemies will know exactly where you are, negating the benefits of Hide.
A Wood Elf could use Mask of the Wild to hide behind certain light obscurement that will appear later in the round (the web spell would probably apply). They would then gain the benefit from being unseen. Otherwise, just Hide on your normal turn.
Use an Object
The general statement applies here; you could now pair a readied Use an Object with any other normal Action (like a full set of Extra Attacks). You could Ready to use a Healer's Kit with the Healer feat to heal yourself or an ally. Note that magic items would not apply here, as they are not activated with Use an Object.
Attack
A Rogue can already use Sneak Attack twice per round by using their hasted Action to attack normally and readying their normal Action for outside of their turn. A hasted Rogue / Ranger with Extra Attack would gain one non-sneak attack with the proposed changes.
Conclusion
If, when presented with several options, one is (almost) always selected, then that option is probably overpowered. Would the proposed changes make haste a must-pick? Sorcerers with Twinned Spell will take it, but they do that anyway. Control-focused casters may choose it slightly more often, but fear and hypnotic pattern are encounter-ending spells that still surpass haste in most situations. Paladins and Rangers who receive haste as an extra spell will continue using it in the same situations.
A Rogue X / Horizon Walker Ranger 9 with haste would receive one additional non-sneak attack after the first round of combat. This is a significant power boost, but it shouldn't break the game. After all, a Gloomstalker Ranger 5 could be making 3 attacks in the first round of combat without spells, multiclassing, or feats! The rest of the Ready use cases are more about flexibility or niche situations than raw power.
Allowing a character to Ready a hasted Action will make the spell more powerful, as will any increase in flexibility. When presented with a modified haste as an option, it still will not be chosen every time; therefore, the changes presented will not make haste overpowered.
Best Answer
Not with a typical amount and quality of potions
In my experience running and playing games, players have a fairly limited supply of potions. In Tier 2, each player typically has one or two buff potions and a small supply of healing potions.
In order to evaluate the change, we need to look at who you are casting haste on.
Optimal targets for haste also tend to be optimal targets for buffing and healing (the vast majority of potion effects). These optimal targets primarily attack on any given turn. Thus, with your proposed change, a hasted target deciding how to use their additional action will most often weigh "drink this potion" vs "attack this enemy once".
So how balanced is this decision? There are three basic possibilities:
Note that I'm not focusing on the ease of potion use before and after this change. Why? Because it doesn't really matter; what matters is opportunity cost. The proposed change certainly makes potion use strictly easier, but does that make it underpowered, overpowered, or balanced? Given that haste already permits a single attack (which we assume is balanced), the determining factor is: how powerful are the potions?
Potion of healing
The classic healing potion; heals for 7 HP on average. By the time someone's casting haste, the party barbarian has 55+ HP and the fighter isn't far behind. Healing 7 HP isn't nothing, but it's unlikely to be worth forgoing an attack. Healing in 5e is largely a waste, unless the target is unconscious. (There are exceptions - big spells like heal and nasty enemies that kill when they drop you to 0 HP.)
More powerful healing potions exist, but they scale rather poorly. A potion of superior healing heals for 28 HP on average, the same damage a single player takes from failing a fireball save. The potion is also Rare, which places it (roughly) at the same power level as a potion of invulnerability. The latter has far more damage-removing potential when used properly.
Thus, I would consider drinking a healing potion an underpowered use of the hasted action.
Powerful buffs
A potion of invulnerability seems like an excellent magic item. Resistance to all damage for a minute! Unfortunately, the tradeoff is skipping (most of) your first turn, since its short duration doesn't allow for easy out-of-combat use. The outcome of combat is usually determined within 3 rounds*. Skipping a third of combat for damage resistance is a hard sell. Skipping one attack, though? That's more like it.
Even longer-lasting buff potions, like a potion of fire giant strength, are more attractive when used with haste. The players sometimes don't know when they'll encounter a big dangerous fight, so they never pre-drink potions. Given the cost of drinking them in combat, even longer-lasting buffs rarely get used.
Thus, I would consider drinking a powerful buff potion an overpowered use of the hasted action.
But wait! If a character drinks a buff potion, you also have to consider the opportunity cost of no longer having a buff potion. If potions are properly limited, characters can't simply drink them whenever they want. With those limitations in mind, I would consider drinking a powerful limited-use buff potion a balanced use of the hasted action.
Conclusion
Your proposed change will certainly increase the power of haste, but the best targets are usually better off hitting the enemy in the face, than downing a potion. Buff potions become much more usable - and thus more powerful - but as long as you don't give them out like candy, overall game balance should not be harmed.
* "The outcome of combat is usually determined within 3 rounds" is based on my personal experience playing in several hundred Adventurers League games (Tiers 1-4), and running Ghosts of Saltmarsh (AL) and Out of the Abyss (non-AL; extended into late Tier 4).
Combat may often continue past those 3 rounds, but the result is a foregone conclusion. Wizard casts fear on the first turn, and 3 of 4 enemies fail? Stick a fork in that encounter - it's done! This effect becomes more pronounced the higher the character level.
This answer pegs the number at 4-5, but that's the entire duration of the combat, including any cleanup at the end. The DMG implies that 3 is typical.