Look up mortality percentages associated with hysterectomies.
Look up hysterectomy complications.
It's linked to early death if ovaries are removed. It's also linked to a whole host of other negative things including certain serious diseases. It ages people.
Yes, she wouldn't have a period after that. Personally I don't think that's a good thing - I also think the complex ways in which it affects a multitude of hormones in your body (and the relation to disease) aren't fully understood.
If she's having problems with her periods she's better looking for solutions to that. You can take things to make periods lighter, I know people who've said it's changed their life. Tranexamic acid. Try implants instead of birth control, etc.
If you have your tubes tied you still get your period.
It doesn't affect your hormones.
So everything else would be the same.
If she hates birth control side effects, there are other options to whatever she's on. There are more options than ever. Also, I guess if you decided to have a vasectomy, she could stop taking birth control, and that would solve that issue.
If she had her tubes tied she would not need to take birth control.
You also says she has bad cramping issues whether she's on birth control or not, so that doesn't seem like the issue. The issue is that she hasn't been properly treated for whatever is causing these problem periods. If she doesn't want periods, there are ways to accomplish that. I know people who haven't had periods for years. Personally... I think that somewhere down the line, that will have an adverse effect on your body - it's completely unnatural, but I know a lot of people don't hold that view. I'm also really lucky that I've never suffered with painful periods or any problems with them apart from they are an inconvenience, so I don't really know what it's like for some people, who may dread it.
It seems like the main issue here is by the sounds of it she has severe cramps and it hasn't been treated properly, I'd look at that first. I have a friend who vomits when she has her period and is literally sick/ill for five days every single month and that is a huge proportion of your life to be affected.
So in a nutshell getting tubes tied does not affect hormones and it does not affect periods.