Spaying is more invasive and is never cheaper IMO. Neutering is not as complicated.
While native rabbits in the US aren't super social, domesticated rabbits are descended from selectively bred wild rabbits in Europe that are much larger and more social than our native buns. They live in large warrens and this is generally why people suggest keeping them in pairs/groups. That being said, setups for them in captivity are much, much smaller than the unlimited space of the wild where they can spread out and give one another space while still living in the social groups they prefer.
Absolutely there is a point. If they are currently together, with the first litter of bunnies, when she kindles (gives birth) she can be bred back immediately. All lagomorphs and rodents can do this. In addition to it not being conducive to stopping the breeding issue, it is also not healthy for a female to be both nursing and devoting bodily resources to a litter of unborn kits. This is the same reason doctors tell women not to get pregnant back-to-back. if she's getting ready to nest, and you're confident the first litter is eating on their own I would separate them and dad in a manner that allows the doe to still interact with them through the wire so that a bothersome reintroduction after the neutering isn't an issue, but so he can re-impregnate her the moment she's through giving birth.
if the male is currently on his own, leave him that way. It'll be much easier and you won't have to worry about baby Jesus rabbits and immaculate conceptions.