Actually you can definitely play around higher AP values since AP boosts what is in most cases, by nature, unreliable. AD is sort of a middle ground here. It boosts basic attacks, so no you can't really play around that. However, some of AD's value (especially on a character per character basis) is put into how much power it gives to more unreliable parts of your kit. A great example here would be Graves. It's totally possible for a Graves who outstats you to lose a trade if he misses everything because a lot of his kit's power is put into his Q and R burst.
I really disagree with this entire part. The basic premise here pretty much says "autoattacks have very little counterplay", so anything that boosts autoattacks has no counterplay. I think that's a fair description of your argument. Well, I disagree. You can punish someone for autoattacking. You can zone them out from it, you can. Abilities carry advantages that autoattacks don't have, and those advantages can be used against autoattacks. That does represent counterplay.
The point is, stat changes don't mess with this at all. Having more AP or more autoattack damage or whatever doesn't give you anything more to play against, because you still play against the enemy champion in the same way. I'm going to play the same way against a Syndra with 0 AP as I will against one with 1,000 AP (assuming I have the same relative strength as them at the time). AP doesn't give me anything to play against. Similarly, I'll play the same against Graves whether or not he has crit, because the key value of "autoattacks are a threat" doesn't change significantly enough for my playstyle to be modified. The only way it could change is if he completely gave up on attack speed and went for a pure AD burst thing where he could barely hurt afterwards.... but he's not going to do that.
If crit was a simple % increase on your AAs and it was priced in such a way that it's gold efficient, then it's automatically better because it's 100% reliable.
Again, yes, it is slightly better, but by much less than you would think.
As for the snowballing with a stacking mechanic, the scenario you are depicting means you're not CS'ing and/or pushing.
It actually doesn't. I can zone someone away from their last hits at a point when their minions aren't dying, get 5 more autoattacks quickly to get my stacks up once my minions die and theirs are at risk of dying, and then zone them off for another few seconds. Their only time of entry is when I have 0 stacks, because even starting a fight when I have half stacks will be enough for me to get a crit by the end of it. I do this right now on live with Caitlyn, so I can completely guarantee you I'd do it with crit.
This could also be solved by making your stacks fall off after a certain period of inactivity.
Not for the laning scenario, no. I only have to zone you off for about 5 seconds to deny major amounts of farm. Have a delay shorter than that and you majorly screw with teamfighting because someone can get zoned off for longer than that. You also introduce the problem of backloading all damage, which has a small risk of weaking carries in the midgame.
My problem here is, this is another small change, on top of all the other small changes we'd need to make this system work, and the end result isn't even better than the % increase.
For assassins, there are very easy ways to make them not want to build crit and/or make them sacrifice something if they want crit. That can be as simple as putting crit mostly on AS items or are as complicated as making new assassin items that are more appealing.
I wouldn't use the phrase "as simple as" to describe designing a lot of new items and only putting crit on AS items (mostly isn't good enough. Even one item is an opening). Those kind of redesigns aren't simple, That's a lot of redesigning that would have to happen. We'd have to rework the AD items that currently have crit, we'd have to rework the AS items, and we'd probably have to introduce multiple new items that are appealing enough to assassins to override the benefits of a guaranteed crit, and then we'd have to rebalance them around their synergies with their new items.
Also, just having attack speed won't stop me from buying a crit item if even the smallest ability to preload crits. I mean, think about it. It's 100% of my AD as frontloaded damage. That's worth more damage than one AD or armor penetration item, and it's not like attack speed is completely worthless just because I'm an assassin.
That's all a lot of work. This really is going to be a hard and long problem to deal with. And that's kind of my point. We'd need a ton of work to implement this system, we'd have to redesign a lot of items, and for what? There's no benefit that we can't get with a % damage increase.
I just don't think it should be RNG based.
Then the % system is better. Outside of big numbers I don't see a single thing the stacking system does that the % system can't do better. Seriously, I don't see a single one. I don't see any pro that the % system can't match with less work and less time consumed. Yeah, we could force the stacking system to work with enough time and effort, but if there are only additional costs and no added benefit, then it's not actually a good option. I think when you really list out the pros and cons, the stacking system has a ton of cons that the % system doesn't have, and it has no pros over the % system. As far as I'm concerned, that means it's not an option.