It could mean only-ness ('exclusivity' would be nice) without implying insignificance. In this situation, it had to imply insignificance too because we're talking about an alt account against a main account.
So "merely" would've been better.
"Drizzy. is merely an alt account, made for that sole purpose." is hence, even better.
"... made, for that sole purpose" is weirdly moving a comma, it doesn't seem right saying it. If you consider the sentence as having two clauses, you'd separate them with a comma. If the comma is placed before "made", none of the two statements would make sense.
"... an alt for that sole purpose" will work fine. I wouldn't use it because in a general context, it looks like Drizzy. is only presently an alt, or that the account might cease to be an alt when the 'purpose' is achieved. The sentence is grammatically correct, but I'd want to avoid the possible technical implication. An alt account would always be an alt account as long as a main exists.