Think about it. What's the actual benefit of Nintendo crowing about "timed" exclusivity? And how many of these "timed" exclusives is Nintendo actually paying for? I think it a lot more likely that developers are simply prioritizing their Switch ports. And I don't think this prioritization is happening because of money or contracts. It's just simple economics.
The Switch has a sizable install base, and brisk software sales. End of explanation. The metrics likely support that a Switch port will be more profitable, and less costly then an equivalent port on XBox or Playstation platforms. The hardware for the Switch is more modest, but it's also based off of the same basic architecture as most mobile devices. ARM development is not exactly costly or uncommon in this day and age. If you can optimize your game to run decently on the average mobile phone, it will run fine on the Switch. And given the Switch's older and weaker hardware, the resolution and framerate expectations are not nearly as severe.
If Nintendo doesn't have contracts with most of these companies, then there really isn't anything to crow about. Claiming timed exclusivity seems churlish, especially if it causes backlash. With no ink on the page, too much of a community outcry could end up changing decisions at some developers. If a developer thinks that their fans would be more demanding of port on a different platform, then maybe they would shift their priorities, and that timed exclusivity could disappear. Why risk it?
Nintendo paid six million for Monster Hunter timed exclusivity, so clearly they do care and are paying (at least in some cases): https://www.nintendo...ivity_on_switch
The benefit of timed exclusivity is that they make a cut of every sale on their platform, and if people are only able to get it on their platform they make more money. Monster Hunter sold over 5M units and they get 30% of every sale, they've already recouped their money on that deal and then some. That's simple economics.
I will give you, there's no reason for them to tout or even disclose when something is/isn't timed exclusivity. Slapping a "timed exclusive" label on things would only encourage people to wait and deter sales of the impatient. I also know for a fact that a lot of exclusivity agreements are NDA'd, so the devs/pubs wouldn't be advertising it either.
I don't think every game that comes out first on Switch is a timed exclusivity agreement and I highly doubt that other devs are getting anywhere near Monster Hunter's $6M. Development often targets the low-end hardware first, and in modern gaming that's the Switch. However, when games consistently come out six months later for other platforms and that aligns with Nintendo's rumored/leaked timed exclusivity window the dots start to connect.