if you cut someone out of your life because you love them, they don't love you, and you've realized they will never be yours?

...even though they try to be your friend?

If you aren't able to strictly like them as a friend, then it wouldn't be healthy.

I've had crushes on friends, fooled around with them, and I attempted to be friends again with them afterwards. Just didn't happen.
I hated it, so I just had to delete them and block them from everything.

Yes it is usually better to cut them out of your life. If you have feelings for the person, and they don't feel the same way about you, then keeping them around as a "friend" will only continually hurt you, and it also might give you false hope.

I agree with ShyViolet

Yes.