You apply it quicker and better, but less accurate
Applying poison to a weapon will last until you either you hit a target, or critically fail with that weapon, but the rogue ability allows you to quickly apply a poison using a single action, regardless of how many actions it would take to apply the poison normally, that lasts for one round (effectively a round and half).
Why is that single action important: Because there are several poisons that normally require three actions to be applied. Most of them to be exact.
Also, you may apply Contact Poison without the risk of poisoning yourself, which is normally impossible to anyone else:
Contact poisons are infeasible to apply to a creature via a weapon attack due to the logistics of delivering them without poisoning yourself.
Finally, they also gain a couple of simple poison dosages to use each day. So, to offset all these advantages, they cannot apply the poison to use later using this action, the poison dosage won't last. However, they may still apply the poison out of combat (3 actions) and have her blade already be poisoned during combat. Later on, the poison won't be wasted on a critical failure (Improved Poison Weapon) either, so it will last until you hit something or until the end of your next turn.
This is unnecessary
I've played at a table where several PCs, across different campaigns and DMs, have had the Lucky feat and I've never experienced an imbalance issue or a feeling that it's overpowered.
Already limited
The feat is already limited in that it can only be used 3 times/long rest. That's a pretty big limitation when the volume of rolls across a day's encounters can be high (both PC rolls and rolls against the PC). In my case, we generally only have 1-3 combat encounters/day and we still had to manage when we wanted to use it.
I just haven't seen or felt that the being able to force a reroll was problematic. And that reroll isn't a guaranteed improvement, either.
Less fun
I would say that as someone who has had the Lucky feat with a character that treating it more akin to the Inspiration mechanic would turn this into something less exciting. It's fun to say "Oh, that didn't work out, but I'm Lucky! Let's try it again!" It's less fun to hedge your bet with an advantage/disadvantage prior to the roll.
More management for the DM and the player
In this scenario, before you roll any die against the PC with the feat, you're going to have to stop and ask them if they'd like to use Lucky.
EVERY. SINGLE. TIME.
Otherwise, there may be a time when they wanted to use it, and you didn't give them the opportunity. And now you're back to the original method of the player saying "Well, you didn't ask, but I wanted to use it, but you rolled. So can you reroll?"
What about the Halfling racial ability?
This works very similarly to Lucky. Are you going to change how that works as well? While it's a special case of rerolling 1s, that's impactful for when the halfling is attacking. Just like Lucky is impactful if they roll that 1.
Sort of works like an upgraded multi-use Inspiration
The way you want the mechanic to work is very similar to that of Inspiration:
If you have inspiration, you can expend it when you make an attack roll, saving throw, or ability check. Spending your inspiration gives you advantage on that roll.
The main difference is that you can also use it against an enemy, which is not how the Inspiration mechanic generally works. We do have a question covering this enemy-focused function, but I can also supplement that by saying we allow the use of Inspiration at my table to force disadvantage on an enemy attack/save/ability check and have had no problems doing so.
This is not to say I'm advocating for turning the Lucky Feat into a modified Inspiration, but that it is an option - just not the one I'd prefer because of the above.
Best Answer
Forgo isn't the best word choice, Assurance works as rolling
The clear intent of Assurance is that you no longer have to actually roll a die, but the results should be adjudicated as though you had. Anything that references "rolling a success" or similar is functionally the same as "getting a success" and Assurance affects either.
Normally I would take words at their face value, but we have to remember that Paizo has a number of writers and has adopted a stance that things don't have to be written exactly the same to mean the same thing (vis-à-vis "rolling" vs "getting"). And we know that Assurance is still a type of roll because it's a Fortune effect.
A fun side effect of this is that Assurance can be negated with a Misfortune effect and vice versa; if you have a Misfortune effect on you, you can use Assurance to roll normally.
Because Assurance is still a type of roll (even if there is no physical/digital rolling of a die), it qualifies for any text referencing rolling a [result] (assuming 10+proficiency is enough to succeed).