I know it's common behavior in games, but let's not take the contrary as bizarre.
It's not so much bizarre as disappointing. The devs know some of us like playing dress-up; it just seems unnatural for them to not anticipate working with the Legion and wanting to dress appropriately.
Why would they give you a suit? If I help the US military, do they give me fatigues to wander around town in? You're not enlisted, boyo.
First off, it's pretty weird that I can't enlist, for a number of reasons I won't bother to expound upon unless you insist

Off the top of my head, there are a couple good reasons for them to give me a suit.
1) Reward for merit. The game itself actually builds up this expectation with the whole conversation with the Centurion. He's all, "My armor proves how sweet I am. This armor only goes to the sweetest of the sweet. Don't you wish you could go do a bunch of quests for Caesar and prove how sweet you are? If you were sweet like me you could get this armor, but you're not nearly that sweet." And so forth. No other well-written movie, book, or game would issue a challenge like that and deliver zero followthrough. The Caesar owes me his freakin life, and what do I get? Experience points and a "good job, stranger".
2) Simple. I agree that for walking around town I might not need it, but on a battlefield, armies wear uniforms to keep from shooting their own people. I don't know what the final battle is going to look like (please don't spoil it!

), but if I'm going to be spending any time walking around near active Legion troops in a live fire situation, I want them to know at a glance that I'm not just some dangerous-looking, unpredictable Profligate woman. I think Caesar would want them to know that, too, especially since I imagine he has a special role in mind for me.