Per the book, he was supposed to die. No cheesy "oh, they are all happy" ending would have sufficied.
Also, we don't see any indication that the woman is the alpha male's woman. Only that they are learning simply because of the fact that Neville has grabbed a fair few number of them for experimentation. The alpha doesn't come to get his woman to Neville's place, he comes to destroy the living.
The plot holes for me started with the introduction of Anna. If she had indeed been at the pier all day, why had she not met Neville who was ALSO at the pier for a fair bit of time that same day, waiting for the zombies to emerge? He didn't just show up, he had been there waiting.
And it just goes downhill from there.
The ending actually is a fitting one considering the Bob Marley song. Keep that in mind

Yes, it was a bit of a cop-out but the manner of his going out goes directly with the song that was played repeatedly with Neville and Sam and Neville's explaining of things to Anna from his perspective.
Neville's refusal of a community is also not far-fetched. He has lived alone for about 3 years. There is undoubtedly some paranoia and pessimism as he has seen his fellow man fall and be exterminated for so long. Couple that with the fact that he is hurt and obviously feverish and you have the perfect recipe for delusional thinking.