Because why not SSJ2? when he handled his brother who at a early age was above him in terms of power as a kid and trunks also who was both SSJ1 levels
As we seen gohan (adult) at based couldn't handle broly so I would be more appropriate to say he went SSJ2 without the electricity couldn't be a design flaw either way it took Goku,Gohan (Adult), and goten to defeat broly with enough blast to reach the sun.
Cell-era Gohan>>Buu-era Gohan. This was confirmed multiple times.
That being said, Gohan's far more powerful Cell-era SSJ self was already wtfstomped by Broly in Movie #8. With that preexisting knowledge, it wouldn't make any sense whatsoever for his Buu-era self to only transform into a SSJ against Broly, given that he was, again, confirmed to be far weaker at the time. In even simpler terms: If he couldn't do shit against Broly as a SSJ during the Cell-era, he sure as hell wouldn't have tried to attack Broly as a mere SSJ during the Buu-era.
I have it like this:
Movie #10 LSSJ Broly>Movie #8 LSSJ Broly~SSJ2 Gohan(Buu-era)>SSJ Gohan(Cell-era)>>SSJ Gohan(Buu-era.)