I feel different from most anime fans in that sometimes I can ignore it and other times it's worth dropping the series. A little fan service and cringe nosebleed scenes are just standard anime tropes at this point. But some anime pushes it so far that, like you said, its jarring and distracts from the story. I've dropped a few shows just for the annoying fan service alone (Fireforce, Fairytale, Seven deadly sins, etc.)

If you are looking for recommendations of shonen anime that have heart, action, and deep characters I would suggest: Mob Psycho 100 and Ping Pong the Animation. Both of these have a weird art style, but they both have a story to tell that leaves a deep impact on you.

That said, anime is a a big medium and there is something that will appeal to everyone (dramas, sci-fi, romance, ecchi, sports, mecha, horror, comedy, historical fiction, etc.) I've linked some helpful anime flowcharts/recommendations that I always refer to when I want to get away from the endless deluge of seasonal anime.

https://imgur.com/gallery/4htwnQ1