They have lots of them (called "chicken bits"). Some of them have BIOS flags, some don't.

It's very very expensive to fix a bug in a CPU, so it's easier to expose control flags or microcode so you can patch it out.

There were CPUs with whole plethora of optional optimizations. For example Cyrix packed their CPUs with goodies, but had no money to test so made it all optional.

https://www.ardent-tool.com/CPU/Cyrix_Cx486.html#soft

https://www.vogons.org/viewtopic.php?t=45756 Register settings for various CPUs

https://www.vogons.org/viewtopic.php?t=30607 Cyrix 5x86 Register Enhancements Revealed

L1, Branch Target Buffer, LSSER (load/store reordering), Loop Buffer, Memory Type Range Registers (Write Combining, Cacheability), all controlled using client side software.

Cyrix 5x86 testing of Loop Buffer showed 0.2% average boost and 2.7% maximum observable speed boost.