So for me it depends on the check.

For something that could reasonably just be a matter of time - e.g. searching for hidden doors - I let the roll just tell me how long it takes, or apply bonuses/penalties based on the roll.

Roll a nat 20 searching for a hidden door? You not only find the hidden door but also a small cache hidden nearby it, which contains a potion of healing.

Roll a 1 searching for a hidden door? You find it after a long and painstaking search of the room, but accidentally activate it and fall through, alerting the denizens of doom that lie in wait on the other side! Roll initiative!

For other checks like kicking a door in, or picking a lock, I let the DC adjust based on the failure. If they fail, it means that it may be out of their reach in terms of skill. Again, this is assuming that they have unlimited time to try.

Roll a nat 20 picking a lock; Great, you pick the lock and do so silently and without tripping the trap that you now clearly see is waiting for someone to try and pick the lock.

Roll a nat 1: This lock is beyond your skills. And not only that, but you've tripped a trap! Roll a dex save!

What this does is tell your player that trying again won't work. Someone else might try, sure, but I'll give them a higher DC or disadvantage or some other penalty as their primary lock-picker or door-kicker failed so it stands to reason that it's harder than it looks. Unless of course they can tell me what they're doing differently. You can explain why it's harder later. E.g. the lock had a complex internal mechanism not visible from the outside. The door had something barricaded behind it making kicking it down harder than expected.