I'm an MSc student considering whether to stay at my current institution for PhD, or move elsewhere. I am aspiring to a faculty position, but want to make sure I have backups, so getting industry experience (internships) is important to me.

My current department is not well-positioned in that it doesn't have "feeder" companies and it is very small. Internships are hard to get anywhere, and would be especially difficult here.

My question is this: Does it make sense to move to a better-connected institution just for the internships? Is this even a thing people do?