OTOH, given the massive publicity of the project, it would be difficult to keep it from getting reanimated at some point...
What massive publicity? You mean the diplomatic scandal over a Federation superweapon, which surely would have led to the cessation of all future development on the project?
No one came out of the Genesis incident looking good - the Federation were secretly developing this scary planet-roasting nuke, and the Klingons were sending scouts into the Federation to steal secrets, blow up civilian and Starfleet ships, and murder innocent people.
With potentially only one scientist alive with the knowledge to continue Genesis - which was apparently a failure, given the planet tore itself apart within weeks - it seems like a dead end which was not pursued further. The political pressure to sweep it under the carpet would have been too strong anyhow.
Besides, the stated aims of Genesis - overcoming food supply and overpopulation - seem to have been solved by the 24th century, with replicators and faster warp drives opening up a much larger Federation with newly discovered habitable planets.