So? You want me to adventure naked? /jk

Paladins don't do stealthy; they go in the front door. Sometimes that's peaceful and friendly, for everything else: DEUS VULT.

That's why they invented pass without trace.

The solution is as follows: the entire party rolls against a DC (typically passive perception though it could just be opposed), and so long as half of the party (round up) succeeds, you are sufficiently stealthy. Realistic? Not necessarily, but it lets a stealthy player do something without having to go off on their own and get killed.