In general, I think it can be a good method of birth control (with the provisos about waiting until the sperm count results are okay), if the couple have decided they have enough children, or they don't want any, and it means that the woman doesn't have to rely on hormone contraceptive pills, because messing around with your body for years should be avoided I reckon, there are health risks. I think I would appreciate it if a man took responsibility for contraception in that way, if we'd completed our family.
However, it can present problems if the couple divorce, or maybe if their child or children die and they want some more, or maybe they just change their mind and decide they want more children after all? Because while it's potentially reversible, it's less likely to be successful, whereas if a couple are using condoms or contraceptive pill or implants or coil, or whatever, then you can stop using them. So it's not something that rushed into, it should be something that the couple are sure about, and they've thought through those issues.
Personally speaking, from a very personal perspective, though, if I met someone who had been married before and had had a vasectomy, even if I really, really liked him, I probably wouldn't be able to continue in a relationship with him, because although I have a grown up daughter from my first relationship, I would like to settle down and start a family, so I wouldn't want to be with someone who had had a vasectomy and didn't want or couldn't have more children, so it would be a depressing thought for me.
(Although if I was seeing someone and we tried to conceive and it turned out we were one of those unlucky couples who had fertility problems, I like to think I would be more accepting, but I wouldn't choose to put myself in that situation, would would accept it if I happened to find myself in a situation where we couldn't have a family, and I would probably want to look into adoption.)