I doubt if a palomar is weaker than a clinch under any circumstances (except faulty execution of the knot). Do some experimentation and see what you find out, I speak from my experiences only and people have different paths through the FF world.
I used to fish trout as a top target species. Frustration over lost trout on super-light tippets is actually what drove me to using the palomar when I was a teen. The difference was profound for me using the same tippet. They could pop the tippet but not the knot.
Doubling the single strand around the hook eye (like the palomar does) makes the clinch a stronger knot. I think they call it the trilene knot or something. I prefer the palomar, much easier to tie.
I have been a winter steelhead junkie for decades, in these presentations a fly ends up in the rocks fairly often. It's pretty clear that a palomar is a stronger knot when you are pulling out from a rockpile.
Other knots are more suited to applications despite possible loss of knot strength, like the non-slip loop which imparts better action to certain flies but needs to be checked and re-tied to keep it strong enough; the turle and double turle are great for loop eye salmon / steelhead hooks and snelling a tippet is a great way to tie hooks for trailers (e.g. coho salmon flies).
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