1) They encourage solo play.
If I level up in a team, I won't loot enough to be able to take my level when my character is ready to. If I play solo, I will just be able to scrape together the right amount of gold for the next level.
2) They break flow of gameplay, roleplay, teamplay.
Having to walk back to town to find a trainer, really sucks. Especially at epic levels when, typically, you're training in places that are far away from everything. If you happen to be soloing,then there is no fast way to get back out to your training, either. It means you spend a good 30 minutes of your session running/fighting your way back to town, and then another 30 minutes fighting your way back out to where you'd like to be training. This also means it's quite time inefficient, it puts a sharp, short halt in the way of teamwork (if, for example, the rest of your team DOESN'T need to head back to town as well).
3) "You have just lost 19,518 experience points."
This just happened, because I spent the last couple of hours grinding for gold so I could take my level. I could have been over half way to my next level by now!
4) There doesn't seem to be a clear reason as to why we have them in the first place.
So far, the one reason I've heard was, "high level players have enough gold anyway." - so perhaps it is to moderate the economy of the server. But then, to be blunt, I look at the trade channel, the last three posts I've made looking for items which, while rare, shouldn't be impossible to find across the playerbase have zero responses to them - there is no 'economy' that needs moderation here.

Why do we have training costs?