Sounds like your player doesn't just want to be the GWF concept, but wants "GWF who can fly", and I'd tell that player that sorry, that concept doesn't really exist in the game unless he wants to multi-class to a caster and get that spell himself. I.e., building a character concept that is dependent on your other players doing exactly what you want is pretty poor form. And a bit selfish.
It's not you being selfish for feeling bad because you have to cast fly on him every combat and not using any of your other spells. It's the other player being selfish. D&D, since day 1, has been a team sport by default. Sometimes your PC will be in a situation where they aren't all that useful and another player gets to shine. Demanding to be the #1 guy all the time is childish and selfish.
I play with friends, not people I treat like I don't care if they have any fun.
This wasn't a problem with easy access to disposable magic items and no concentration mechanic.
It isn't the player being selfish. You seem to think it is ok that a game create a situation where a melee martial can't enter combat due to something like the concentration mechanic, lack of easily available disposable magic items that provide an actual
fly spell, and high mobility creatures that can full attack and move their full flight speed thus avoiding the melee martial complete. It creates a situation where the melee martial has no chance of living or attacking effectively. He becomes a fifth wheel because he chose a fairly common fictional fighting archetype and another person chose an archetype that can attack at range.
What you want me to say to my friend is the following, "Never choose to play a melee str-based martial ever again that can't cast
fly on himself (Eldritch Knight, Arcane Trickster). You know dragons and demons get to move their full speed and attack evading your melee attacks. I don't want to have to cast
fly on you. I know str-based thrown ranged weapons only have about a 30 foot effective range and it's hard to come by magic weapons that will make you do half of the already lower damage you're doing with throwing weapon, but them's the breaks. Don't ever choose like classic archetypes like Battlemaster fighters with greatswords or barbarians. You're going to make things hard for us at high level against powerful high mobility creatures like dragons and demons."
If you feel like saying that to your friends, have at it. I like to work as a group and have fun as a group. At the moment casting
fly on my buddy's greatsword wielding battlemaster not only allows him to get into combat against dragons and demons, it's also a smart move. It would not only be selfish of me not to cast it on him, but poor tactics considering he can do good damage with his blade.