This does not address the real-world case where built-ins will not compile in some valid code contexts. It is not "better" to do something that literally doesn't work. No one is doing this for fun, it is working around a well-known limitation in current compilers.
Because it is an unfortunate limitation on built-ins that reduces their utility, fixing this is on the roadmap for most popular compilers.
On top of that, the popcount built-in will always compile even if there is no instruction for it, as it can generate fallback code. It actually does so for a naive invocation of gcc or clang for x64 as the original x64 IS did not contain popcount. You need to pass some arch that supports the instruction, or -mpopcount to explicitly enable it. Handling all those builtins properly is tedious.
Because it is an unfortunate limitation on built-ins that reduces their utility, fixing this is on the roadmap for most popular compilers.
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