These are the new rules:
1. Only one Pokemon are you allowed to have, not six.
2. You aren't allowed to battle if your Pokemon knows any TMs or Tutor moves. You are allowed to only teach it level-up and breeding moves.
3. No items given to them.
4. No legendaries - they are too strong(some of them but anyway).
5. No psychic types - in real life, they would be unstoppable as they could just control their opponent from a distance and kill him. Unfair.
6. There would be Pokemon leagues like heavyweight, lightweight etc just like in boxing. Thus, Pokemon would only fight other Pokemon of their size. Blissey wouldn't go against Gyarados due to tremendous size difference.
Oh Pokemon Trainer UV, what you are talking about is EV training. In real life, of course stats would count. Pokemon would have their base stats, its just up to the trainer to train them and make them even tougher.
Blissey has the most HP meaning that she is tough and can tolerate a lot of damage.
Rampardos has the most Att(non-legendaries) thus he can hit the hardest.
'Stats' exist in the animal kingdom too, it's just that animals' stats aren't measured.
An elephant and a whale have more HP due to their size.
A hippo has more Def than your dog because it has thick hide and bones.
A buffalo has more Att than your cat because it's stronger.
Stats would exist and count. Blissey would be a soft round thing which would be easily damaged(low Def) but it would still not faint and keep on going in spite of the horrific injuries(high HP).
If you would take your Charmander with you at the gym then you would EV train it for Attack. If you take him running with you then you EV train him for HP(kinda like stamina).
And you simply can't make him endure its weakness. A weakness is a weakness. His tail flame will always be put out in the rain.
Still Blissey can't be beaten by any of your Pokemon guys :D Charmander(or Charizard) doesn't have a chance against her neither does Alakazam(which is banned due to the rules).