Your argument does not make logical sense. By your definition there:
- John plays Joan Baez tunes on his acoustic guitar for his grandma's birthday every year (who pays him $25 for the "gig"). John is therefore a Professional Musician.
- Seamus has a band with his 4 high school friends. They play the local bars twice a month and get paid $400 total per gig. Seamus and his band are therefore Professional Musicians.
- Bob, who is running sound for a gig at a back yard party, asks Billy Joe (no sound experience) to cover for him for 15 mins while he takes a leak and says he will pay Joe $20 to do so. Billy Joe is therefore a Professional Musician.
You cannot just rubber-stamp everybody who performs for a measure of time and gets paid a random sum of money a Professional Musician (as much as some here would like to imagine themselves to be).
The IRS has their own definitions which (naturally) suit themselves in collecting taxes. Therefore, in the "tax world" (or "speaking in tax terms"), those definitions apply... but musicians don't perform music in the "tax world", they perform music in the "music world/real world", so the appropriate definitions must be used.