I don't think it's odd at all. As long as one isn't creating a single point of access to progress around it along with making it uncertain whether any character will actually notice it... it actually serves quite well as a reward for character/build choices. In D&D 5e your score is your indicator, the only difference I see between what you are stating in your post and what D&D provides is that it's not an off/on indicator but instead an indicator with gradations. The DM always has the option of deciding no check is necessary or that a characters skill is high enough that there is no uncertainty. A roll only comes into play if there is uncertainty in whether Joe would notice something... Many like that uncertainty, that feeling of chance affecting the game world, something which an on/off indicator with set results just doesn't provide.
But now imagine a dungeon full of traps, like Raiders first sequence. Using this technique won't really make that very exciting. Your character progresses through the scene randomly setting off or not setting off the different traps depending on what the check value is to find any given one (he may find all, some, or none). In fact in the scene Indy FINDS every single trap. The process you describe would IMHO just mean you'd take 'X damage' (maybe none if you can see/disarm/avoid all of them) on the way in and out. I guess the 'boulder trap', if it triggers, would still be interesting, the rest less so IMHO.
I'm not sure your assumption about how Perception is used with traps in 5e is accurate, at least if one is following the advice and rules in the DMG. The basic structure of trap interacion as laid out in the DMG is...
1. Detect it (Perception check/Passive Perception/Any action that clearly reveals the traps presence) NOTE: Usually some element of a trap is visible to careful inspection
2. Understand it (through skill check or description)
3. Disarm/Foil it (skill check or improvised actions)
The DMG goes on to discuss different Danger levels of traps (Setback/Dangerous/Deadly) and how to set them. As well as complex traps (They have an initiative, a turn, 1 or more actions and creates a dynamic challenge).
If a DM is choosing not to let characters detect or interact with traps via fiction well they are ignoring the DMG advice and system on traps. that's a failure of application of the system not a failure in the system itself.
I'm not sure how what I described diverges from this. You either detect the trap, or else you will surely set it off, right? I assume a Perception Check is the gate for active searching to be successful. I suppose there is room for the party to devise some specific approaches, assuming the GM uses that option.
I think perhaps you are assuming how traps work as opposed to having actually read the section in the DMG on them in 5e as almost everything you are stating in the above section of your post is a part of discovering and disabling traps in 5e. Again if a particular DM chooses to ignore the rules and advice well that's on the DM not the rules system.
I think the rules CAN BE exactly as I've described. This is not going against them AFAIK. In fact I've been through at least 2 5e modules, and that was exactly how they were handled, a check to determine if you saw the trap, and then if you did you got a check to see if you disarmed it. Even if the character picks a specific action related to the fiction describing the trap, a role was called for.
Part of the problem here is that 'the 5e rules' is not a thing. At least not in this regard. Half of 5e's 'rules' are too vague to say there 'is a process/rule' and a LOT of them are optional, including everything to do with skills and checks! Technically you could run a subset of 5e, just the most core non-optional rules, that would handle it essentially the same as OSR. I'm not exactly sure how a thief would work in that configuration, so I don't know if they would still invoke the skill system or some other mechanism to adjudicate 'thief abilities'. If it is the current system, then at least some of what I described is still accurate (and similar to how many people interpreted F&RT even in AD&D even if that was incorrect strictly speaking).
So, yeah, maybe, depending on what you call '5e rules' you could be partly correct, but I think my analysis still largely stands and doesn't involve some gross misrepresentation of the game. It certainly DOES represent how a lot of D&D has been played, and how many modules seem to think it is played.