By the same token, QB throws to the other side of the field, no advantage, so I would pass on throwing the OPI. Watching the film in real time, the pick and the eventual throw are pretty far apart in terms of actual time of the play. No different that a hold away from the point of attack -- not every foul deserves a flag.
I don't think "no advantage, no flag" applies to situations involving potential OPI.
Take a look at AR 7-3-8 XVI:
On a legal forward pass beyond the neutral zone, A80 and B60 are attempting to catch the pass thrown to A80s position. A14, who is not attempting to catch the pass, blocks B65 downfield, either
before the pass is thrown or while the uncatchable pass is in flight. RULING: Team A foul, offensive pass interference. Penalty15 yards from the previous spot.