I might be misunderstanding but what you’re talking about is basically just failures of a DM.

DMing osr style games requires being more than a simple automaton applying the rules. The systems are simple to allow you to spend your energy elsewhere. I’ll use OSE as an example as that’s what I’m currently DMing.

Let’s take perception. Firstly if something matters from a fun perspective it should be obvious. For example, if overcoming a trap is fun then the overcoming should involve play, not dice rolls which are there to abstract over tedious or uncertain play. For example a large magical fire blocking the corridor requires no perception but will involve a lot of experimentation to find a way past.

Or if we are wanting a perception roll like event: Lets say players are stuck and have no ideas for finding a secret door they think is likely there. Who are the characters? not their stats who are they? Ok someone was a farmer prior? huh ok. Give them a clue to follow like “hey Jake the farmer, you notice the air in this room smells familiar, there’s a maddening scent of petrichor which has no place on a dry stone chamber like this one” see what happens. Alternative if Jake asks for a clue ask Jake to describe some way in which who he is applies to the context and set an ability check for a true or false clue. Suddenly a lack of rules is freedom for players to build up their character mythos on the fly.

Likewise for player skill stuff. No reason a player needs to narrate a conversation anymore than swing an actual sword. If a player asks me if they can make an impassioned arguement based on legal precedent, a sense of justice, and the illegitimacy of a ruler who cannot protect their vassels to the King’s guard then they make such an argument as appropriate to their character’s level of skill.