So if your greataxe wielding Fighter stumbles across a magic greatsword, you're just going to toss it aside because you only use one weapon: a greataxe?
nope... I would say it depends....
let me give you some examples...
kurt had no magic items but a rapir refluffed as 'elven longsword' he comes across a +1 maul... nope not taking a +1 str two handed weapon over his finesss 1 handed he has
Matt and Joe both have longswords and shields and we come across (in diffrent rooms) during a dungeon a +1 short sword and a +1 sheild... since having a magic weapon helps the party even if it lowers the damage die they decided to keep the items togather and Matt gets them so he can hurt things that need magic and is a bit extra protected... the next set of games we don't get any magic weapons but by level 5ish we come across a holy hammer... it doesn't have a plus but at will you can change from blut damage to radiant damage... that hammer sat unused until we gave it away... by higher level both had magic longswords (I think matt actually had a +3 one at the end)
my barbarian... this one is me as a player I started with a great axe, and game 2 or 3 we found a +2 spear... in this case the world had magic shops so I claimed it and traded it in later for a magic great axe
craftsman +1 short swords... so we had a DM who had a dozen "enemy" stats in a note book and would just reuse them with slight tweeks,,, since his rogue/stalker/assasin (depending on whn thos stats were used) had 1 short sword attached to his/her to hit, we found dozens of +1 short swords... we joked they were mass market craftsman short swords.... we DID have 1 melee character take one, other then that the rest of our melee characters just chose to wait for bigger weapons, and as such we had at least a dozen at one point while people didin't have magic weapons...
my current artificer uses a gun (that never needs reloading and is +2 thanks to an infusion) or my cantrip I call razor webbing (thorn whip refluff) or if close my shock web (lightning lure) but often just punch with my thunder punch (I have two weapon fighting so I can add damage with off hand so I have 3 full attacks)
I am the tank of the party (and thanks to my magical power armor that is fullplate+2 helm of awwarness made of adamantine... I do a pretty good job. We find magic weapons all the time. Since we don't often use weapons we mostly just collect them or give them away.
Have I played characters that NEED to switch, sure it happens, but not often, I mean even random drops of items you can pretty much find what you want.