I'm broken on this one.
On one hand, yes, it kinda defeats (most of) the purpose of the punishment if the person who intentionally left just alt-tabs and plays a different game while they wait it out with little to no inconvenience.
On the other hand, forcing someone to stare at the LPQ box seems like an unnecessary punishment to those that got slapped with the LPQ because of several recent internet/computer/irl problems.
Maybe make the suggested prompt-version LPQ as a punishment escalation after the current, non-prompt, version.
Edit: As pointed out to me in this thread chain, the 20min LPQ is one of the later punishments that leavebuster hands out after several previous punishments.