This game was made to allow you to LEVEL every class, but it is not designed to allow you to gear and PLAY every class (at least not in raids. You can do the petty content like dungeons, since gear isn't even that important to victory there). You pretty much have to pick a main every major content patch and stick with it, to gear it up to be able to clear the newest raid content. If you are gearing two or more jobs at once, then you're shooting yourself in the foot, because you will not be as competitive as other players, assuming they're equally skilled but better geared because they focused on a single job while you wasted your lockouts on two+ different jobs. Weekly lockouts force you to either be gimp or play a single job. Of course, as a patch becomes old and stagnant, you have the time to gear up other jobs, but by then, you're already defined in your group as "the monk," or "the warrior." Your team composition is already set, for the most part, with a couple of swaps for certain fights.
What alts do is allow you to split your focus so that you can actually play and enjoy the other roles/jobs you wouldn't get to, otherwise, because you're stuck playing those one or two specific jobs every time. Alt A can level and gear up Paladin, doing its weekly lockout. Alt B can for some stupid reason, decide to be a dragoon (joking), and gear that up. Alt C can play scholar, cuz why would you want to heal when you can DPS and make the WHM or AST do it, instead (Joking again, unbunch your panties). This game was designed for alts, really, but instead punishes you for having them. It's not really any different than any other MMO that locks you to a single class per character, it just gives you more illusions of freedom.
Of course, a lot of people (myself included) level three crafting alts to 60 in everything so that they can craft absolutely anything (stupid crafting specialization). Again, another reason we should have more freedom with alts, because if you WANT to be the go-to crafter within your circle of friends, you have to play at least three different characters anyways. I get that they wanted the specialization to force people to only use three crafters, to promote more economic ties... But the serious crafters don't do it that way, anyways. The big timers all play three or more characters so they can specialize in everything, simply skirting around SE's restriction nonetheless. Of course, it's inconvenient because you have to either use a grand company chest to trade stuff between your alts or have a friend willing to trade back and forth for you.