Let's say that you want to take that alt up all the way to 50 rather than just for cross class skills. At 50, you're going to run into a giant contradiction between the armory system which encourages switching classes / jobs and performing many roles and the endgame system which discourages that altogether with a weekly cap on myth currency (which limits you gearing up more than one job) and Coil having lockouts (which again limits gearing multiple jobs). So you either focus on one, half-focus on more than one and take forever to gear up, or just accept that if you play more than one class that doesn't share gear, you're going to have very poor progression.

Then of course is the problem with actually leveling to 50 with most of the quests gone, dungeons not giving enough exp compared to FATEs, and generally FATEs being the only thing worth doing. I'd have been depressed leveling my alt (PLD, which of course shares a lot of gear with WAR, otherwise I wouldn't have done it...) if I was in a situation like the TC and saw empty FATEs.