Ignoring any coordination, you have a 33% uptime on it anyway. If the cor himself has Wildfire, there's no coordination needed or damage lost to give yourself the +10% (outside of the very first fire shot), since you have a 45 second window to use your QD+WF before you're losing damage (since the charges share a cooldown time or whatever...do 1 shot, it doesn't matter if you use 2nd shot right away or 40 seconds later, it comes back up at the same time either way. Past that, any time you have a rdm CS-nuking, it shouldn't be too much to ask, if a cor is there, to put up the appropriate shot, or any time you're planning to zerg something that includes anyone planning to do elemental damage.
As a side note, if you have 2 corsairs with said boots, it wouldn't be a very large loss to initially stagger QDs, as long as they use them somewhat on cooldown, to put uptime at ~66%. While I wouldn't sit there and hold TP for it, like you said, there are a lot more practical applications than you are giving credit for.