As I use my IRL identity, I can't change my NIP-05 at will, at least I shouldn't move it from my own domain.

However if you are seeking privacy, then yes, your NIP-05 is kinda irrelevant.

Is identity even real?

My name should have been David, but my mum forgot to tell my Dad as he escorted me with a priest, in the ambulance trying to save my life by taking me to a specialist hospital. The priest baptised me in the ambulance and asked my Dad what he wanted to call me 😂