My response to the OP:
Here's how I see things:
- OHKO moves, Evasion modifiers, and "hax items" all bring an additional element of luck to the game.
- Allowing them ultimately means that you will be winning/losing a greater proportion of your battles down to luck.
- I play competitive Pokemon to win. The majority of the time, the "having fun" part for me is inherent in winning. However, if I lose in a really great battle where it all came down to skill, I still have a great time. But the majority of times when I lose, it's down to hax, and then I'm not having fun. Similarly, if I win a battle due to hax, I also don't feel too happy, although I feel admitedly better than when I lose to hax, as I'm sure is the case for everyone.
- What I conclude from the above two points (and keep in mind this is just for myself that I'm speaking) is that allowing OHKO moves, Evasion modifiers, and "hax items" will ultimately make the game less fun.
I would think that there are many people who agree with my statements above, perhaps to varying degrees. Now to add on:
I mentioned that for me, having fun is inherent in winning/losing a good, or at least a fair, battle. Of course, I also consider team building, talking about Pokemon on Smogon or over MSN, reading analyses, among other things, enjoyable components of my collective competitive battling experience. For all of the above, strategy is what makes them interesting for me. There is no luck in team building, people don't discuss luck when considering the viability of a new set. All in all, luck is not one of the reasons I enjoy playing Pokemon.
Personally I wouldn't mind playing a "metagame" where the amount of damage a move does is set, and there are no critical hits. Move accuracy is something different in my eyes. Between Flamethrower and Fire Blast, you have the choice between accuracy and power. This is a choice you get to make before battle during the other "fun parts" of Pokemon (team building, discussing certain sets, etc.). Ultimately it's something you can prepare for, whereas critical hits are not.
Really, I think the only need for critical hits is against Pokemon who stat up defensively with moves like Cosmic Power or Calm Mind. Otherwise such strategies are significantly harder to beat, and without crits you may go into stall wars much more often. So in my ideal world there would be a formula which determines your critical hit % chance based on the defensive boosts your opponent has, starting from 0% (so under normal circumstances critical hits don't happen).
Now I know that this is no longer Pokemon but really what is Pokemon, at least the Pokemon that we play? What makes it okay to ban OHKO moves but not ban crits? Obviously the fact that banning one is easy to do whereas banning the other fundamentally changes the game, as it's not something you can just "turn off" ingame. And banning crits on Shoddy would no longer make it a Pokemon simulator. But it would be interesting to have a mod server with the above implementations.