Personally I don't see the problem with PPs. It's just experience. You can spend it on skills or stats. Who cares? Yeah, you could get rid of them and training skills would be more or less the same, since the system was updated so that skill training grants enough experience to buy the next level. If you choose to blow all those PPs on stats instead, then you're out of luck. You'll have to get more experience to level your skill. That's just how it works. Nothing wrong with it.
If you get rid of PPs, skill training will be more or less unchanged but stat training will be pointless. Anyone with rich friends or a rich alt can get 400 in all stats in an hour. That's not how the system is supposed to work. You're supposed to have to consciously allocate your experience to stats/skills in order to develop your character. Changing the way stats are raised is an option, but that'll take a LOT more work. So the whole "just get rid of PPs and everything is better" argument is kinda silly. It requires so much more work than that.
About trainers, I would LOVE the ability to buy multiple levels at a time. Right now, having to track down the trainers for a given skill is the most frustrating part of the leveling system. ESPECIALLY when you're training multiple skills at once (like herbal/alchemy or a weapon and armor) and the trainers are in different cities. SOOO much wasted time and tria traveling back and forth...
Yes, having the choice to buy multiple skills at once slightly complicates the system, but I think the benefit to the players FAR outweighs this. Maybe a compromise: only have this option available once a skill reaches level 20 or so. This means new players won't have to worry about it. They can spend the early time learning the basics of training. Then once you hit a certain threshold the trainer can say something like "You've been progressing quite well. I think you should be able to handle multiple lessons at once." And from then on you can buy up to 5 at a time.
In terms of implementation, whenever you try to buy a skill that's already trained, you can have a pop-up box say something like "You have already received training for this skill level. Would you like to purchase the next one for XXXXXX tria and YYYY PPs?" If they say yes, you can have a little indicator next to the progress bar with a "x2" or something. If they buy more it'll say "x3", "x4", "x5" and each time they level up the number counts down. Once it hits zero they need more training.