I don't like it.
- It delays your leveling up unneccesarily. Sometimes you gain enough experience in a dungeon to level-up, but you can't do the level-up because you have no training hall handy. So you'll face the boss with less power than you could.
Also, that can go to extremes: I once was short 200 points to next level (AD&D2) and couldn't level-up (especially since the whole group refused that I got an advance on my XP. And I was a level below them). After that, we went into a lenghty dungeon. After the first fight (it was something rediculously easy) I had enough XP, but no means of training, so I had to go through the whole dungeon a level below my comrad adventurers. I was really pissed-off at that time!
- It is illogical. The characters' experience and capabilities are represented by their XP and level. You get XP for killing monsters, solving puzzles, overcoming traps, and solve other problems, earning more experience. If you have enough XP, you gain a level. But that is an abstraction, just like your age: you aren't really 21 for a whole year, aging a whole year on your birthday, but it would be to complicated stating you age in months, days, or even seconds. In the same way, you get a little better every time you do something that gives you XP, but it would be silly to have a BAB of 7.5478 for a single stroke and 7.5479 afterwards, so you have a BAB 7 for a long time, and then you havea BAB of 8 (same goes with all the other numbers). But just as the change of 21 to 22 years is really the culmination of a year's worth of aging, gaining a level is really the culmination of a long time's worth of getting better a little bit at a time. So leveling up should happen when you earn enough experience, because you actually leveled up a little bit at a time the whole time since you leveled up last.
- It is illogical. Why should you wade through a horde of enemies (and survive) without becoming a better fighter, but if you fence half an hour with that teacher, you suddenly are a better fighter?
- All the 1st-level characters probably probably trained for months or even years, only reaching 1st level, but after a couple of days out in the wild, they will become 2nd level. And after a year, they could already be 20th level! That's because learning from a teacher in a training hall will only teach you that much. If you want to be really good, you have to earn experience, and that can't be done within a protected hall. No, you must go out and face danger, overcome real foes, and solve problems your fighter's manual didn't tell you about.
- If that weak of training in the hall could accomplish what two months out ther in the wild could not (that is, advancing a level), all those kings and what not could cram their quests where the sun don't shine! I'd stay in that posh training hall, exercising all the time, and some months later, I'd be 20th-level, without a single second of danger of limb or life. And laugh I would at those stinking, tousled jerks who go out into the wild, missing a good bath and pretty lasses for days, only to gain power!