If you have to ask this question then the answer is almost certainly no. This isn’t to say it’s worth it for nobody – but the groups a gaming phone is worth it to are people who can afford one without blinking and people who already know they really really want one.
Most mobile phone games are only worth a few dollars because no one will pay more than that for mobile games other than via gatcha mechanics (and gatcha mechanics interfere with games, making them worse). There are a couple of exceptions (GenshinImpact being one) but when I googled 2021’s best mobile games the first list I found included things like Final Fantasy VII (a game from 1997), Stardew Valley (a 2d Pixel Art game), and Downwell (an iphone game from 2016).
These games are not bad games. Quite the opposite. But what they are is low spec games that simply do not need the power of a gaming phone. You don’t need a gaming phone to play them – and getting a gaming phone is like getting a silver dinner service to serve McDonalds or boxed mac and cheese.
If you want a better mobile gaming experience unless you’re already playing one of the very few ultra-high budget games that go cross-platform and can eat all the processing power you give it you won’t get much out of a smartphone for gaming. Instead you’re much better off keeping a decent phone and getting a Nintendo Switch as that has a lot of actually big and deep games created for it. And has input mechanisms (joycons) that allow for precise input timings – or it can play touchscreen games.