anon theory:

the WH will burn, but the WH will not be overrun. It would be really bad optics for a bunch of rioters to be shot (even though thats what they need). Maybe a sleeper on WH staff sets the fire, or rioters use flame thriwer, I dont know, but I cant see them over running it. Rioter, burn the Capitol building too, that's about all it's been good for for the last 50 yrs or so, firewood. With all the noxious gas in that place, it should burn for days.