I wouldn't go so far as to say they're intended to be clownish. I think that's overstating it quite a bit.
But I will say I think we're intended to see a degree of hubris, brashness, and perhaps a tad lack of planning in their stratagem. Perhaps its different from the perspective of a Brotherhood player, since you're working with them quite closely and helping them in their tasks. But from the perspective of an Institute player, I thought the invasion of the Commonwealth looked a bit poorly executed.
Maxson and the Prydwen come flying in, flags flying and loudspeakers blaring announcing their arrival to everyone in the Commonwealth. Making this grandiose show of force and Brotherhood power (that's admittedly very cool)....and then....nothing.
Brotherhood scribes can't find the location of The Institute. The attack stalls, and The Brotherhood just sort of falls back into default operations of scavenging for technology and hitting raiders and mutants. All the while losing men, supplies, and aircraft the longer they are in the doldrums. The two major engagements they have with The Institute before the attack on Logan Airport are at Mass Fusion and Bunker Hill. Both of which seem to be unplanned (on the part of both parities) and just sort of a matter of "Oh [censored], guess whose here. Attack!"
Maxson may have been a bit too eager to take the fight to The Institute. Without fully understanding what he was up against. Which sort of seems in-line with his character. Bold, overeager, and headstrong: brave perhaps, but also overconfident. Seems like they planned for a much more traditional military campaign, but The Institute doesn't fight traditional military campaigns, and has no need to. Which left The Brotherhood a bit unprepared for what followed when they couldn't immediately find them.
Just my thoughts anyway.