Oh plenty of the Leaguers can be stealthy as hell when they want to be. J'onn especially. But it's not just "how stealthy can they be?" it's "why are they being stealthy in the first place?" Maybe a Leaguer has to be sneaky because the League needs to get intel out of a guy. Maybe they need to crack into a computer without anyone knowing. For the first goal, you'd send J'onn; he can sneak in, read the guy's mind, and be gone. For the second goal you'd send Bruce because he's better with computers.
There's also the matter of what kind of detection they're avoiding. Pressure plates in the floor? Thermal sensors? Atmospheric sensors? Motion sensors? Magical wards? Different methods would rule out different Leaguers.
And what other goals does the team need to meet? While someone's being sneaky somewhere, is there some trick that requires a telepath or shapeshifter elsewhere? Or someone to evacuate civilians? Or whatever?
It doesn't matter if the Leaguer is the only person capable of doing a thing or the one who does it best, you just find a cool thing for them to do and then write a reason for them to do it, and if necessary a reason why it's *them* doing it instead of someone else. If they're the best at doing the cool thing then great, you can really amp that scene up and push the boundaries. But it's not required. All that matters is that everyone on the League (or at least everyone in that issue and story) has a cool thing to do, usually one that leans into their strengths as a character.