Why is the "free play" not stopped for defensive penalty?

The most often that I've seen a "free play" is when a D-lineman jumps offsides. The play doesn't stop and the offense can basically do whatever they want with the knowledge that they can just accept the penalty and redo the play if it goes wrong. But why doesn't the play stop? If an offensive player false starts, the play stops immediately.

I feel as if defensive offsides and offensive false starts are the analogue of each other. But then, it's unfair to the defense that the offense gets the opportunity to run a "free play" when the play just stops during a false start and the defense gets nothing similar.

Let's say the play continued after a false start. The defense might use the "free play" to rush 8 guys and hope for a sack. Or have their D-line move back and not rush and basically hope for a pick. All with the knowledge that if it doesn't work out, who cares. Just seems unfair to the defense.

Honestly, though, I feel like the most fair outcome would simply be for the play to stop on a defensive pre-snap penalty. The whole "free play" concept seems inherently unfair.