I've seen this about 3 times now. Two were older men who had been married many years, within months remarried. Another was a woman whose husband of 20 years (who was about 20 years older than her) passed after about 5 years of ill health. She was still in her 40's, and also was remarried within a year. The woman...too soon to tell. His brothers and sisters still include her in family gatherings, but his son (her step son since he was a kid), no longer speaks to her. He's hurting and angry.
But it ended up being a huge mistake for the two older gents. They simply rushed things too much to avoid being alone. The women turned out to be completely incompatible. They were looking to replace their wonderful wives, and ended up with nightmares. Before one of them cut the lady loose, he and she had alienated his entire family. Sadly, he also ended up losing everything financially. She even went after the house he and his wife had paid off years before. She didn't get it, but he had to sell it to pay off the debts acquired during his short marriage. Mind you, he was living only off social security to start with. So he went from just-making-ends-meet poor, to destitute.
I wonder about DH. I sometimes think he couldn't make it by himself -- so I could totally understand, as I want him to be happy. I would just want him to respect the grief of others around him (our children, my family), enough to at least not remarry in under a year if it distresses those people. Mainly, though, a decent length courtship would be mostly important to me to keep him from making a mistake. It takes time to know how compatible you are with another, and I want him to be with someone who will treat him as the treasure he is
On the flip side, after we lost our two pets, neither of us can even think about having another pet without getting emotional. If that's too hard for him to contemplate, I'm not sure he could even come close to a replacement wife!