Selecting and then using passive CPU coolers. I am saying both the bracket and socket are important when choosing a cooling.

For example, when introduced there was no aftermarket passive cooling available for the AM4 socket.

Really of the 5 considerations “Does it fit the mounting bracket?” is probably the least important. Fitting the motherboard and case are mandatory. Fitting the socket and TDP have a little wiggle room. However, with mounting brackets you can generally get something to work as long as you keep firm contact and it does not wiggle around it’s fine.