Is it common to have canine teeth removed and Braces fitted? (photos)

I have two canine milk teeth that are nearing the end of their life (I am 30). I considered implants but need braces to make the gaps bigger. The orthodontist has suggested extracting the teeth and using a brace to push my back teeth forward. I've been researching and apparently it's a no no to remove these teeth, I just wondered how this will affect the way my teeth look and would implants be a better option? Also is there a risk the gaps won't close properly? I've attached photos of my teeth