That is your opinion, And I respect that.
Guess we agree to dis-agree.
That is cool.
There must be at least a million electricians and electrical engineers that are wrong.
What would grounding the system hurt ?.
Without the source being grounded The GFCI may be tripping balls. And could be smoking the attached items.
Having the proper Ground will not hurt, and will protect all equipment involved. Including the user.
Have a Great Day.