It seems pretty destructive as the enterprise had to go to warp to get away from it.
Well, she had no shields. If in full repair and outside the disrupting nebula, she might have weathered the Genesis wave just fine for all we can tell.
ST:FC doesn't look too illogical to me; it's more in the "Ooh, they didn't tell us everything - how alien and mysterious!" category. One possible scenario has the Borg coming in for their second attempt at assimilating Earth and its technological secrets; finding this too difficult, they launch plan B, which is to destroy Earth's ability to develop these Collective-threatening technologies. And this requires preventing Earth from creating the Federation, which is easily accomplished by killing the one man who can lift Earth from post-WWIII apocalypse by making it worth the Vulcans' while to come and help. As a side benefit, the Borg win a free (if now uninteresting) planet that they can use for whatever they do with planets.
Or then Plan B was always their one and only goal here, as they had already decided the Federation was too much a hassle to assimilate and too big a nuisance to leave be, and had chosen to nip all that in the bud with a bit of time travel. They still went from Borglandia to Earth in the 24th rather than 21st century because... Well, perhaps simply because they wanted to assimilate the latest Starfleet technologies and tactics before they nullified Starfleet altogether, and a suicide run with a Cube would accomplish that. Or then because back in the 21st century, there were obstacles between Borghome and Earth much bigger than mere Starfleet.