I'm not going to request multiple stealth checks for attempting a single thing (ie - if you sneak into a camp, that's going to be one stealth check, regardless of the number of sentries) because otherwise you make failure very likely, even with competent PCs.
Definitely. This is one reason why turn-based* exploration rules are a good idea, because you handle the whole turn with
one check.
*it's not really necessary to use strictly "turns", you can cover a whole area as just a single turn of whatever length you decide
That said, more complex stealth scenarios are more difficult to adjudicate fairly: you want to stick to one roll, but you also want the PCs to be able to react to things they observe and take more or less risk. I think if you're keen on running an extended stealth scenario and not just have it fail due to lots of rolls, you want to come up with something more complex: the existing rules just suck for that kind of thing.
Well I wouldn't say they suck, but they do have problems, at least all those I mentioned: passive vs active, distributed vs concentrated, retried vs one-shot.
You are suggesting some very complicated house rules for complex scenarios, while I am suggesting something which is still pretty simple, only "one step more complex" than the base rules, so to speak
The point is, a check distributed over a turn does not prohibit to also allow some specific checks. You can decide to allow a general check to "be stealthy", "search for traps" or "look around carefully" AND also allow a player to check a specific door for example. It's up to the DM to always decide if they get a roll or not, but the
combination of turn-based tasks with ad-hoc specific tasks can help you against all those problems:
distributed vs concentrated: the turn-based check covers anything the player may overlook while the specific check rewards a player who has the right intuition; turn-based checks only remove the reward, and specific checks have the risk of prompting some players to start check everything at every step
retries vs one-shot: the turn-based check already implies a certain extended amount of time (which may in fact implicitly include retries) with the outcome being known only at the end; it doesn't encourage retrying when the player sees she has rolled poorly, at least not nearly as much as the specific check that is described to take 6 seconds (in fact the turn-based check has a benefit similar to those house rules used by many, where each retry takes a longer time to complete, except that here the time is not increased but it can be made long enough in the first place)
passive vs active: the turn-based check is narratively similar to passive checks, without the issue of removing randomness (the DM can still remove randomness if she really wants... just decide there is no need to roll in the first place) or having an active attempt being actually worse than a passive check
Really passive checks should be considered separately depending on whether they are against fixed DC or an opposed roll. Against opposed roll they are actually fine (as long as the opponent is rolling normally), because the essentially change the skill contest into a single check vs DC, which is fine (the two work basically the same, unless you are using different degrees of success, since an opposed check has double swingy-ness). Against fixed DC they totally remove randomness, but if you remove randomness then why are you even wasting time thinking about what kind of check you should be using? At best you can use passive scores to "gauge" what kind of challenges you should handwave and declare an autosuccess, but then for consistency you should allow autosuccess on the same things also when the player actively tries to do them (which most DMs don't).