Simple question--Can a solo only character get a mount?

I solo'ed my main job (Monk) all the way to 50. Aside from two levels I got in 1.0. It's easily do-able. I didn't have the story completed in 1.0 and I never unlocked a chocobo or a license in 1.0. I honestly just walked everywhere. When I started ARR I used porters to get everywhere and just walked. Well this past week I took my Lancer through the storyline and unlocked my license by getting 2,000 grand company seals. Easily done with doing Fates. It's easy. Solo'd it all except the needed dungeons. I used duty finder, got them over with and did everyone else alone. So yes! You can solo most of it, everything else is duty finder!

Yes, I've soloed exclusively till now as well. (...crossing my fingers, hoping that a possible FATE XP nerf does not occur...)

But I didn't want to pass along any specific misinformation about the mounts.

While some parts of the game would be considered solo friendly (like the aforementioned FATEs), not allowing soloers to use mounts definitely would not.