Splitting CPU lane to x8/x8 is supported at least. Just mobo manufacturers don't want to implement it as a dedicated slot. It seems that Alder Lake no longer support x8/x4/x4 sadly.
I would be very surprised if the silicon doesn't still support 8+4+4 operation. I suspect the lack of available motherboards with this config comes down to the expense of getting a PCIe gen5 signal to reach the third slot. It may require both the extra mux and a redriver or retimer.
Perhaps why they dropped the support is because the reason you wrote? Still I wonder is it possible to have Gen5 x8 and Gen3 x4/x4.
Sort of. support is "Up to 1x16+4, 2x8+4" [1] so could be used as x8/x4/x4, the remaining 4 lanes are unused in the x8, as there are 20 PCIe lanes on the CPU.
[1] https://ark.intel.com/content/www/us/en/ark/products/228441/...