It's a trade-off, and it depends upon your campaign.
A more action-oriented, chain-of-thought, plot-point-to-the-next, mile-a-minute kind of campaign would feel bogged down by training rules. They don't want to bugger with some NPC mook just to get to the next HD. When you're camping overnight on the cusp of war, you really can't be bothered to run back into town and fork over some gold so some old codger with a wooden stick can beat you upside the face a few times for your extra hp. It's just going to interrupt the flow.
A more gradual, one-adventure-a-week, slowly-revealed-metaplot, plenty-of-non-killing-NPC-interaction kind of campaign would greatly benefit from training rules, since it gives the PC's a good reason to go about in the town, make connections, and gives them NPC's to care about (usually a good thing). Far from bogging down the adventure, it's how they spend the time they're not saving the world from evil -- that doesn't happen every week. Spending that week doing nothing but fighting an orc or two shouldn't really give you a level, but conversing with the Duchess doesn't really give you BAB. Here, training helps tie the PC's to the world, while giving them a reason to get better at combat for doing non-combat things.
IMC, I use a sort of 'class tree' that allows them to train in classes and abilities related to the ones they already possess without a mentor. Feats are minor enough and rare enough that I can allow them free reign -- even if the Fighter doesn't know how to cast magic, if he spent his third level feat for Empower Spell, that's fine. His character trained himself with what it would take for his character -- not every Empowering works the same way, after all.
But if that Fighter wanted to take a level in Sorc, he may have to take a level in a different class, first (specifically, in this case, Aristocrat). This is to represent the change in direction he's taking. Or, he could find a Sorc mentor, and just level up as a Sorc next time.
Since I start out my PC's at level 5, they can pretty much have levels in everything they're expected to eventually.
Of course, I also provide incentive for mentors in the same way I provide incentive for organizations, churches, and the like. I introduce new feats, spells, prestige classes, etc. specific to these organizations that those outside of the organization do not have access to. So that Fighter may have a mentor in the Sodkillers, an organization that preaches survival of the fittest. Because of this, he can take several Sodkiller-specific feats that those without such a mentor would not have access to.
But if they have no interest in Sodkiller feats, they can simply be a Fighter, and have no problems with it.