May one who shaves on a regular basis, shave on chol hamoed as well?
Good question, but no.
While the reasoning you stated would not allow a carte Blanche approach to shaving on chol Hamoed, nevertheless in certain circumstances it would be permissible. The Rav has allowed it when, for example ones child has a bris (brit) on chol Hamoed or other such “tzorech”. The determination of “tzorech-need” should be determined by consulting your Rav.
Would a potential chillul hashem ex. a highly formal workplace in the medicine field) where patients are having a first impression of their physician and a representative of the staff of the hospital be a “tzorech” according to Rav Abadi?
If you’re employer feels that way, then shaving would be ok because you already shaved before YT