There is no extra cost.
Therefore it would have a an e-fuse or a regular old 'current' fuse -- which is just passing a calculated amount of current through an intentionally thin interconnect so that it burns away.
1 - https://static.techspot.com/articles-info/1840/images/2019-0...
Of course, this could be evil Intel playing its tricks again but financially speaking removing AVX-512 do have tangible benefits to them in the form of increased microcode for the rest of the instructions (I want to see the detailed Alder Lake errata, maybe there's indeed a bug in another instruction that requires more microcode to implement - AVX-512 is an easy sacrifice for that).
Once you advertise a feature, you have to support it. It'd be pretty damn hard for Intel to explain why lower tier i5 and i3 CPUs have a feature that higher tier i7 and i9 SKUs are missing unless you jump through hoops via hardware (e.g. disable E-cores) or software (e.g. making sure to only run your process on P-cores).
If you want to experiment with AVX-512, just get an older CPU. Much less hassle for both Intel and their customers in this particular case.
An therein lies the difference. They advertise the feature, which is something they never did for AVX-512 on Alder Lake desktop. If they advertise a feature, they cannot disable it without getting into legal trouble.
If you get K-SKU, you get an unlocked multiplier. That's guaranteed by Intel and that's were their support begins and ends.
They cannot do the same for AVX-512, though, because that's not possible in their heterogeneous architecture. There's currently no desktop OS that supports different CPU cores (as in capabilities) on the same socket (or even board).
Such feature would require kernel drivers, thread schedulers, and possibly compiler toolchains to be modified for at least Linux and Windows and that's the kind of support Intel would need to provide. They did provide a thread scheduler, but to my knowledge that didn't include any AVX-512 related logic.
Nobody asks them to enable both AVX-512 and E-cores. People want them to not disable the mode that already works today -- P-cores only mode with AVX-512. There are no OS or driver reasons to not do that.
That hypothesis is not credible. They can simply declare a feature is unsupported, and even that using it voids some guarantee. I mean, look at how overclocking is handled.