Are there any real advantages to a headless guitar?
Believe it or not, yes.
Headless guitars look goofy and always have, but they've been around for a long time, so players do buy these things. Above is a Spade HH, but believe me, there are plenty of other choices available - some of which are quite affordable.
The advantages to using a headless guitar
Lighter in weight (typically)
Most headless guitars are purposely built using smaller bodies since they don't need to counterbalance the weight of a headstock since there isn't any. As such, overall weight is usually quite light.
Absolutely no neck dive
I'm pretty sure the headless guitar is the only one where I can absolutely say it will never have neck dive. The majority of the weight is always in the body and there are no heavy tuners on the neck, so yes, one could say you are guaranteed no neck dive.
More often than not you get the same scale length on a headless as you would on a full-bodied electric, but because the body is smaller and there's no headstock, the instrument will fit in more gig bags. The lack of headstock also makes it shorter and lighter, so it's easier to carry a gig bag on your back when walking around with it.
Nobody wants to play it
This sounds like a negative, but it's a positive. Players unfamiliar with headless guitars are literally afraid of them. They see that weird looking guitar and think, "I'm not touching that thing." This is good, because you don't want other people touching your guitar, right? Right. Chances are pretty good whenever you bring the guitar anywhere there are people, they will of course want to look at it but not play it. And that's a-okay.
The only real disadvantage is the tuner setup, namely for when they wear out. Tuner parts will be more expensive. And that's assuming they're even available for your particular headless guitar. However, given that tuners take a very long time to wear out, this isn't much of an issue.
Generally speaking, the best type of headless electric guitar to own is one that has no vibrato system on it at all, as in hardtail. No vibrato means no vibrato system to break and give you a few extra years out of your headless guitar as long as you maintain it properly.