He'd be weak to range and strong against people who get in close.
Yeah, I got that.
The vast majority of melee champions with a gap-closer only have 1 gap-closer to use, which generally makes them heavily commit and gets them stuck next to whatever they jump on.
Aurelion Sol having a mega-Sunfire cape when that happens would make him extremely difficult to deal with as a melee champion.
It's one thing to have ways to deal with situations like knocking enemies back with his ult, stunning them, comboing Rylie's with his orbs to kite enemy melee's with great ease.
It's another to make Aurelion Sol just flat out win all melee engagements.
A general design pattern that's pretty prevalent in LoL is that a champion tends to win a fight if they maintain their maximum range from a target, where they'll loose to a champion with shorter range maintaining their max range in a straight up face-tank fight.
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However: if you outrange someone and don't let them smack you, they do 0 damage to you and you can kill them without taking damage.
If this dynamic didn't exist: more range would always be better than less range no matter what.
What I'm trying to say is this:
For Aurelion Sol to beat a melee champion, he doesn't need tools to win in a melee vs. melee fight. He just needs to maintain some distance from his opponent.
Making his damage stay at a fixed distance only serves to give him weaknesses that no other champions have.
Given how many long-ranged champions get destroyed in melee range by melee champions, that's an extremely common weakness.
High skillcap is not supposed to hinder a champion at all levels of play. Regardless of skill, it's still far too easy for any enemy with at least one movement ability to dodge his main form of damage reliably.
The unfortunate reality is that pro-play is worlds apart from casual play, and differences in play skill change which champions are worth playing and which ones aren't.
It's in Riot's best interest to balance champions around the level where there full potential is realized rather than balancing for a lack of skill.
With 120+ champions: a lot of players also have very different tastes in the difficulty of a champion's kit. Many players would like an Envoker champion to show off with, and mages like Aurelion Sol generally appeal to that demographic. If you want to play a champion that allows for a good display of skill and makes you look smart when you play them well, they're balanced around having a dedicated fanbase that plays them well.
With only 4 skills and 1 innate on most champions in LoL, it doesn't take a whole lot of effort to really get the hang of such kits.
I understand that you think he should be incredibly easy to counterpick and hard to play even against immobile champs (who generally have more range to make up for the mobility that his sustained-type damage requires they lack), but that doesn't sound like a healthy champion for a solo lane.
I don't think any champion should be easy to counterpick.
LoL lasts ~33 minutes, things that should be decided on a coin flip should usually last in the 1 minute range like a hand of Poker or a slot-machine pull.
Every champion should have oppertunities to succeed even against their counterpicks, and Aurelion Sol strikes me as a champion that has a lot of oppertunities to do so.
His ult knocks enemies backwards into his orbit, and if a melee tries chasing him and is slightly to far away to land their melee skills they'll get pelted with orbs. Sol also has pretty solid manaless wave-clear with his passive, which is useful for dealing with melee champions like Zed and Yasou, and Sol's roaming potential with his flight rivals that of Quinn and Twisted Fate if Sol just wants to ignore his lane opponent and force 1-man advantages across the map.
My issue with Sol pulling his orbs in is that it really removes an interesting counterplay dynamic against Sol, and makes Sol more of a hard-counter to a lot of melee champions with no real tradeoff in Sol's kit.