The flanged plug is a UL White Book requirement
Aside from approving safe equipment, UL has a second unrelated role: they are the author of the appliance safety standards (apocryphally known as the "UL White Book").
The manufacturer doesn't want it on there. It's there because enough people got maimed or killed by appliances that didn't have it, to warrant UL changing the standards. Aand you can bet in the panel meetings, the manufacturers were banging their shoe on the table trying to stop it. But safety prevailed.
So your argument of "It's stupid and inconvenient" has already been debated and rejected by experts.
I have some guess as to why, having been bit by USA plugs that pulled half out of the socket on a power tool. But it may also have to do with not wanting you trying to use 2 tools at once or trying to drag around a second cord that's going to somewhere else.
Yes. It is a reject feature designed to inconvenience you.
And you can modify the appliance to remove it (options 1 and 3), but if you get hurt, you'll have trouble with your insurance claim. And if you hurt someone else, you will be in a much worse place to mount a civil or criminal defense.
Your best bet is probably to use an intermediate length extension cord in the middle.