Disclaimer: I am by no means an expert as far as medicals, their issuance or their denials are concerned.
Having said that; you posted on a public aviation forum and therefore I’ll give you my opinion for what it’s worth.
I think you’re omitting a step in your thought process and your argumentation.
The medical has been denied for you having a fobia which is characterized by an ‘unreasonable fear’.
For butterflies or needles or heights.
Instead of being at the most uncomfortable there is a level of ‘unreasonableness’ to it.
That’s the disqualifier, not the needle.
You’re forgetting blood tests and mandatory inoculations for pilots flying internationally. Just to name two examples of the top of my head.