Using NEMA 14-50 with 60A breaker
No philosophy: Code is data-driven
Code is the result of analysis of systematically collected data about actual  electrical accidents as they happened in the field.   It’s the nature of science that you must take the field data as it comes, and not try to force it to conform to some notion of what it should be.
In the case of 15/20A, the data has shown that there’s no problem there. Keep in mind, UL was a partner in developing that use-case in the first place, by requiring as a condition of UL listing that everything from receptacles to appliances all play nice on a 20A breaker, unless they are on a dedicated circuit.  In that case UL needs the breaker to conform to the device ampacity.
In particular, UL requires that every 15A receptacle be rated for 20A internally.  And obviously 15A appliances must show they fail safe on a 20A breaker.
Conversely, data has shown that when “the big stuff” (40-60A) is mis-fused, trouble follows.  The closest thing I can see to a “philosophy” is “little things have little trouble; big things have big trouble.”

Another aspect often overlooked is how NEC 110.2 (must use approved devices, i.e. UL) and 110.3(B) (must install the device according to its instructions) intersect with UL’s listing standards.  UL approves the instructions as part of the product’s listing, hence 110.3(B), and those instructions are the scope of the design review and testing. When you misuse a device off-label, you’re in uncharted territory. No one can vouch for the safety of that device.
By the way, the cheap Chinese switch you linked violates NEC 110.2 right out of the box, since it does not meet the basic standard of “Approved” — it lacks a UL listing, or any competent NRTL competitor like ETL or CSA.  It is illegal for stores to sell such a thing at retail; Amazon exploits loopholes in our consumer protection laws to sell it. Send it back as defective; the lack of a UL mark, a thing required on anything sold in the US, makes it defective.
Amazon denies responsibility because they say they’re only a “platform” connecting independent sellers to buyers, and the sellers also use Amazon’s billing, warehousing and shipping system.  This is hollow, as far as I’m concerned.
Our best advice is to never buy AC mains equipment on Amazon.  It’s either unlisted junk, or wildly overpriced because of the realities of how Prime shipping is paid for, and the fact that most electrical gear is both low value and quite heavy.  Just work with your local electrical supply or home store, many do curbside pickup.

It isn’t constructive to “overthink” Code like this.  What possible endgame is there to that, except deciding to ignore Code because the reasons are stupid?  That’s a mistake because its premise is wrong: the premise is that the Codebook is full of rules both smart and stupid, and that it’s worth figuring out which is which, and that a novice is capable of this distinction. Every aspect of that premise is wrong.
I can tell you that everytime I’ve looked deeply into the reasons for a particular rule, I’ve seen several of them, and they interlock with other aspects of Code to provide multi-layered protection.  A Code deviation will have unexpected side-effects.
The right way is easy and cheap
The easiest/cheapest way to implement that is actually a subpanel - $20 panel, two $9 breakers (50A and 60A) and you’re Code legal and done.
You’re not actually required at that point to interlock both loads, but if you really feel the need, you can choose your brands carefully to find one that has a $25 generator interlock in a box size you like.  If I was min-maxing for price, I’d look at Eaton, as Square D “QO” is pricey and Siemens’ cheap interlock requires a 12+ space panel (which might be a virtue of its own actually, because you can put other loads there, heck you could power a whole wood shop, presuming the Tesla is out of the garage when you’re making sawdust).
My advice is send that switch back, and slap a subpanel there with or without interlock, and with or without extra space for other loads (not to be used concurrently with the charger, of course).