Know assembly in great detail? No. Know what is assembly and which piece it makes in computer system and how it's related to other pieces. Ofc Yes.

And then every programmer I guess should also know how the processor is doing branch predictions and the microcode....

How deep down should your bog standard web developer know?

Yes, at one point I did write x86 (and 65C02 assembly before that)

Then we get into the whole “Mo one person knows how to make a pencil.”