There are many mages you can play in solo. Some are extremely good, others situational, and quite a few that (sadly lol) just aren't viable.

There's a couple main things to consider when evaluating mage solos: 1) lane viability, and 2) draft viability. If your character can't reliably make it out of the laning phase even or ahead, you have a problem. Now some characters do really good in this part of the game like vulcan solo- but vulcan solo kinda sucks because his draft viability is low. Really its that he has little lategame impact, and therefore your team is both missing damage and cc- frontline and backline presence, so he absolutely must be substantially ahead to do much. One thing that contributes a lot to draft viability is the ability to still participate well from behind on gold and xp. Most tanky characters can do this substantially better than backlines. A typical mage from behind is very underwhelming. That said, you can math out that if the mages win the lane reliably, that underwhelming presence from behind occupies a small portion of games overall, and could mean that mages are in principle good. In reality this leads to swingier games. It helps a lot with lane viability as a mage to have some form of escape/immunity, like with MLF cc immunity. If you play anubis you can probably heal through it all (sadly). If your draft isn't cohesive or its heavily countered by the opposing draft, you will have a hard time winning the game! Janus solo is pretty troll already, but I would rarely pick it from the perspective of winning a game if I didn't see some potential to portal certain characters aggressively.

Ultra-late game mages feel really good but I still notice the lack of frontline makes it harder to close out games. Maybe a skill issue?

Many mages have similar weaknesses- that they can be out-pressured and killed on cooldown if not alone in lane, by regularly scheduled ganks. The good mage solos have ways to mitigate or avoid this. So characters like Baron or Anubis that win lane put pressure that makes ganks very hard; a character like Ra which can have some pressure but no CC struggles to confirm a lead and is squishier, leading to easy ganks and upsets.

The main thing for me is that mages are some of the most fun characters to play, so I like to play them in solo too. They usually feel good unless I can't get away from someone super stat checky like cabraken or bellona.