No

It does not work well to spend the XP budget on a lot of much lower level opponents or a small number of much higher level opponents.

The ability to hit the creatures also matters and also greatly depends upon the level of the characters. You should attempt to keep the levels withing 3 levels of the party, otherwise you will quickly make things too hard or too easy.

Monsters or traps more than four levels below the party's level or seven levels above the party's level don't make good challenges. They're either too easy or too hard, even if the encounter's level seems right. [pg. 57, Dungeon Master's Guide]

I've honestly found 3 to be the magic number in my games, otherwise the players get easily frustrated that they are constantly missing the high level monsters. It is better to use an elite or solo monster if you want to make it a challenge.

I suggest looking at the template designs on page 58 and 59 of the DMG.

Preserve Player Agency in Role Playing Games

While "DM decides" is a standard tool to keep play moving, removing player agency for what players decide to do can turn role playing into roll playing (letting the dice drive everything) and lead to low player satisfaction. The best way to deal with this is to role play the situation.

Ability checks are not saving throws.

You are right: most players will feel cheated if they are forced to do something they didn't choose to do (player agency) that isn't the result of a failed saving throw. Ability checks are similar to, but not the same as, saving throws. (DMG p. 237 and p. 238).

Saving throw fails can lead to players doing things against their will, but they are being influenced by some sort of power ... something like magic.

Examples:

• The Fear save (failed) due to a Dragon's power to instill fear causes the character to flee rather than fight.

• Failing to save versus the Umber Hulk's Confuse power can lead to characters running off, standing around, or even attacking someone in their party.

Ability check is a test to see whether a character succeeds at a task that he or she had decided to attempt.

Note that it is the player initiating something: player agency in action (which may fail anyway).

Compare that to a Contest (p. 238)

A contest is a kind of ability check that matches two creatures against each other.

If two NPC's are in a contest, the players can watch it play out as part of a scenario. Rolling for the result is an option you have ... or you can play out the scenario based on how you want to set up the follow on challenge for your players.

PC to NPC contest? As your question suggests, is it because the player initiated action, or a course of action, or is it a result of a DM initiated course of action? If the latter you are already driving the narrative: why roll? If rolling dice helps you get a feel for how strongly the NPC reacts, then the dice help you role play. If it is to create a saving throw for a social interaction that forces a character to act in a certain way, you may be headed to the railroad station.

What happens when a thug tries to intimidate a PC?

The DM's role playing skills come to the fore. If you set the conditions where the PC feels that she needs to choose a course of action, or feels threatened because of what the thug can do, or who his friends are, then role play the thug and the setting, then let the player choose. Otherwise, you can end up in a situation like this:

DM: "You feel intimidated."

Player: "I go ahead and do it anyway, he doesn't scare me."

DM: "You can't, you are intimidated, he won the intimidation roll."

Do you want to be the engineer on that railroad?

• Scene: the PC bard is meeting a thug in a warehouse near the river docks. She is following a lead, and has been told to "come alone." (The wizard's bat familiar is flying high cover while the wizard hides/remains invisible at the extreme end of range.) Thug arrives with two associates, both of whom have heavy crossbows loaded. Thug's line of conversation is that bard is messing with stuff not her business, and she needs to buzz off. Bard (player agency) tries to role play a diplomatic quid pro quo deal with the thug, offers information, help, services, cash, something. Here, a social skills check for Persuasion makes sense: you want to gauge how well the NPC receives this unless you have already decided that he's not interested, in which case no roll matters.

Let's say the persuasion check fails.

• The thug now threatens the bard with something more than harsh words if she doesn't mind her own business. (A passive Perception check about now to see if she or the wizard/bat detect the other three armed ruffians hiding behind some crates of mining equipment would be timely. Picking up on that is further intimidation, or a sense of threat).You don't need to roll for whether or not the bard feels intimidated: she'll either take the hint or not. Once again, her player agency is preserved, and you set the conditions for her to operate. What she chooses will determine whether or not there is a fight, or she gracefully bows out and looks for other leads. (If you want to roll for your own benefit, to see how aggressive, scary, or intimidating the thug's trying to be, that's something I did for years as a DM: let such rolls help me with flavoring the role playing. )

Social interactions between the PC and the NPC need to be in the hands of the player as much as possible. The NPCs are your tools for creating the environment and the challenge.

On pages 244-246 of the DMG, "Roleplaying Interactions" walks you through starting attitudes of NPC's, Conversation/Interaction, Charisma checks, and role playing. The details includes reactions and DC's based on the creature's initial status: Friendly, Indifferent, and Hostile. It also provides advice on how to use your body language and voice in enrich the encounter.

In Summary

The DM role plays these interactions, rather than relying on dice since this isn't a saving throw scenario. You can let the dice help you shape the role play of the NPC.

Why?

1. It's part of the fun.
2. Preserve player agency wherever you can.

Coda

I had a DM years ago whose theory on dealing with players was "give them enough rope, they'll hang themselves." He was mostly right. We got ourselves into all kinds of scrapes on our own volition by making decisions regardless of the signals he was sending us. Player agency to the limit, and immense fun.