Players can't actually bend rules though or even abuse them. The only one who has control over the rules is the DM who is tasked with arbitrating between the rules and the players.
I'm sorry, but this is quite a naive view. I've seen many, many instances of players bending and abusing the rules, even including nasty behaviour like threats or verbal violence on top of persisting ruleslawyering. Not every DM knows all the rules by heart, or are strong enough to resist a powerful ruleslawyer, or are actually willing to clash.
Yes, theoretically, in 5e (but it was way less the case in 3e for example, with the player-centricity and the complexity of rules), the DM has all the tools, but is he willing and able to use them, I don't think it's the case all the time and with all the tables. I'm looking in particular at all the people who are saying that they play RAW, where it's such a nebulous concept in 5e that it's easy to discuss for hours on interpretations.
The player in this thread is asking if the wolf can work together with the PC for a bonus to passive Perception, not abusing the rules.
And I will accept that as the basis for discussion, while at the same time warning that the type of abuse exists, especially on what is (despite what you write below) by far the most valuable skill in the game and the one that is so critical for survival at some tables.
Your interpretation of the rules appears to be, like many DMs, too generous which makes passive Perception overvalued. It's not always-on radar except in combat or setting up for combat (i.e. determining surprise).
This is wrong, both RAW and RAI. For example in the RAW, the stealth rule that I have given to you show that it applies completely out of combat for hidden creatures, and it's therefore always on. As for RAI, here are the exact words from JC in the podcast on stealth: "It makes sense going back to passive perception. This is, as its name implies, passive.
And it's considered to be always on, unless you're under the effect of a condition like the unconscious condition that says you're not aware of your surroundings that really the practical effect of that is basically your passive perception is shut off.
Passive perception is on basically whenever you're conscious and aware."
And I agree with that, and that's the way I play it, just as with passive insight, which I use a lot in social situations (in particular to avoid the "is he lying ? I want to roll insight" annoyance).
Players do have to declare their actions, whether they are one-offs or repeated actions. And some of those actions can be mutually exclusive with other actions. To do otherwise incentivizes maximizing Perception beyond what the game likely intends. To then suggest it's somehow wrong to maximize Perception in that context is a little weird in my opinion. The DM in this case sets the stage for it happen and then judges the player when they do what they are incentivized to do. Why wouldn't I want to detect creatures, traps, and secret doors much of the time with very little opportunity cost and no risk? That's a great deal if the DM is running the game that way!
As written above, your interpretation of passive is not inline with either the RAW and the RAI. Obviously, as a DM, I can and will certainly give disadvantage or even make it an automatic failure in certain circumstances, for example depending on environment (lots of noise, smoke, etc.) or players action, for example if they are completely absorbed in some task. But these are exceptions rather than the rule.
There are examples in the travelling rules, but note that these are already specific cases, as mentioned in all the campaigns that we have run in 5e, we have used these for just a couple of weeks when playing ToA, because in most of the cases, there is nothing to navigate, no map to draw, no tracks to follow and certainly no foraging, or there are NPCs able to do this (for example, in Avernus, the characters are travelling with their army, or in a huge Infernal War Machine with devil servants, etc.). Or we just gloss over the travel to focus on the story and on the nuggets of action.
We're talking about traps and secret doors, right? Those are both things to be poked and prodded to figure out how they work and, in the case of traps, disarm (or at least bypass in some fashion). I'm not sure what you mean as to uncertainty about how interesting it is. Why would you include content in your game that isn't interesting?
I want them to be interesting in particular in terms of suspense and danger, but also cleverness about thinking that they might be present, but optionally poking at them when none of the former elements exist reduces them to almost nothing.
Further, I don't see why this invalidates other characters' abilities to interface with the environment. Everyone is free to declare whatever actions they want while traveling the adventure location. There's no need for the DM to make any special preparation for highly perceptive characters either. I certainly don't. If you're keeping watch and in the front rank, you might avoid surprise and see the traps - great!
No, with what the player is asking for, it's not "might", it's "will", and it therefore invalidates all the choices of other PCs, since that guy will one-man all these activities. By the way, that is the problem with optimisation, it widens the gap and shuts other people out of segments of the game. And yes, it's often about combat, but not only, I've seen it done quite a bit in the social pillar to shut other players out of discussions, but also like in this case in the exploration pillar.
For the second bullet, it seems to me you are ignoring certain rules for reasons that are unclear when it comes to how you handle Perception, thus creating a situation where it is more useful than intended.
As demonstrated above, YOU are the one ignoring the RAW and the RAI with your personal interpretations.
Don't worry, at our tables, we shift as much as we can to investigation, but still this is mostly for story/searching purpose, in terms of danger perception is still absolutely king.
To correct for this, you then have a social agreement that nobody should then avail themselves of the opportunity by investing in Perception accordingly unless they have some kind of good in-character reason for it (which is easy to just make up in my view). It seems easier to me to just run Perception as it says to and everything else will fall into place.
@Seramus has helpfully posted a number of the related rules to take into account.
Again, as demonstrated above, you views about what perception says are the ones which are incorrect, both RAW and RAI. I'm not saying that you are wrong to change them that way in your game, but please leave the "you don't know what you are doing, read the rules" tone out and apply it to yourself first.