ASM and Performance L4 typer virtual server

None of the performance profiles are going to support ASM. You need full processing of the HTTP protocol for ASM.

There's VIPs like performance HTTP, but truthfully they are pretty rarely used except for very specific use cases and don't support basic things that are almost always used.

You can always try to apply an ASM profile in the security tab and see if it lets you. For ASM, it won't let you apply it if the correct HTTP profile isn't applied.