This is very interesting idea and worth exploring more. Would all potions start the same and have all possible effects in them? Or would there be different kinds of potions that have different starting set of effects?
I was planning for different potions to have different overlapping sets of effects because it is more interesting.
In my opinion (and I think it's more widespread than that), the identification aspect of roguelikes is slightly tedious and is usually just another boring part of the early game. What you're suggesting would stretch it out into something that stays with you as long as you have the patience to play.
That is interesting, what it is that makes identification tedious and boring?
Presumably, you're talking about a game in which you collect a large number of items. You mention the example of potions, an item type one usually collects in tens to hundreds (even thousands if you can buy them in stores) in a given play. You suggest a system in which their effects are randomized and you use some other kind of skill or item to cull certain possible effects. This seems to you to be fun, but I would suggest that the right way to think about this culling process is as partial identification -- what you've really said is that in order to be sure what you have, you need to partially identify it several times and this must be done on a case by case basis.
The way this will likely go down is the following: Players will need reliable effects for dangerous combat and random effects will only be used in these situations in desperation or at the beginning of the game (so the system creates a kind of scumming behavior). Outside of combat, there will be a certain amount of tolerance for the randomness you're talking about, but it will depend heavily on implementation (for example, if removing an effect means replacing it with another, maybe some randomness would be tolerated, but if it is just removed from the list and other effects' probabilities are adjusted to compensate, then probably not). This will lead to scumming to get particular effects and waiting out undesired ones (unless you throw in permanent negative effects, which will again reduce tolerance for randomness).
I think this an idea that sounds fun superficially (something I would've liked when I was 8 and couldn't get a character past dungeon level 16 in moria), but when balanced against the player's desire not to lose results in tedium (scumming, constant partial identification) and removal of gameplay through the player's (correct) judgement that potions must be used extremely conservatively because 1) it takes a lot of time/resources to turn them into something useful and 2) the ones that haven't been given adequate love and care are useless.
(Obviously there are ways to fiddle with the idea on the margin, like removing effects from stacks of items, removing effects in bulk, etc. It's still going to be tedious compared to the standard potion identification game. You might say that it adds control to the kind of potions you have at the end of the day, but if you want that, then make an alchemy/crafting system.)