Put me in the "no need for training"* camp. (I was briefly a player in this campaign, and for the record also told the DM I wasn't in favor of the training rule -- but since I was leaving I chose not to make an issue of it). XP, levels, hp, BAB ... they are all metagame items that describe how much real-world experience a character has. So if "Level" is a metagame concept, why require a character to get formal training in-game? Why penalize a character in game for a metagame concept? If you're doing your bit during an adventure -- swinging a sword, disabling traps, whatever -- aren't you improving your craft? I'm also, as a DM, willing to assume that during "down time" -- whether around the campfire at night, or during the days/weeks/months between adventures -- characters are exercising, studying, sharpening swords, whatever to improve their skills. So further "training" time is unnecessary. And if you aren't giving out treasure like 1E treasure charts, you probably don't need the gold sink, either.
But different styles for different DMs -- this by itself wouldn't keep me from joining a campaign.
*Most of the time. I can see a case where formal in-game training could be required for certain narrow circumstances. Specifically, when a character wants to develop a skill or ability that he/she couldn't possibly have "figured out" on his own, or developed during down time. For example, the fighter who decides to multi-class into wizard, when there is no wizard in the party to learn from during "off-screen" down time. He might be able to figure out how to Whirlwind attack on his own, or he might be especially devout and eventually gain clerical abilities on his own, but suddenly learning to read magic probably isn't going to happen. But then, I'd expect that players whose were really into playing their characters would work these sorts of skill developments into their roleplaying.