Why not demasiado instead of muy?
My guess is it began as a politeness thing. Instead of say something “it’s too big” (e.g. your head or whatever) it’s less upsetting to say “it’s very big”; implying rather than saying what you think. Over time people just “knew” what you meant and accepted this secondary meaning as normal.
It’s less common to use “muy” as “too”, but it is used. Both WordRef and Collins dictionaries also apply that meaning (too).
WordRef defines as a principal translation, with one of three translations:
muy (adv) 1. (mucho) very (adv)
…2. (demasiado) too (adv)
…3. (con participio) greatly, highly (adv)
Collins gives two examples 2. (2nd meaning) (=demasiado) too
Ya es muy tarde para cenar. (It’s too late to have dinner now.)
Es muy joven para salir contigo. (She’s too young to be going out with you.)
you can use both. They have more less the same meaning here.
I think it’s just as used as demasiado for “too”