I open A LOT of support tickets with Box as I'm the primary escalation point for support in my enterprise.

After every Box support ticket is solved and closed by the Box tech, I get an automated "how did we do" survey email.

I get that you guys want customer feedback but forcing it down customers' throats for EVERY ticket that is solved is not the right approach. They just become repetitive and get to the point of being annoying.

I've found a solution to get around this annoyance by creating rules to scan for common subject line text and deleting these messages before they land in my inbox. However, the fact that I, as a customer, am forced to find "workarounds" is telling that your survey process is more if a hindrance than a helpful way to improve support. And, for this reason, this leads me to provide NO feedback.

I think a more professional way to request for feedback would be through:
1) Rather than being reactive (after tickets are closed) being more proactive by having your VP of Customer Success send out a generalized support survey emails on a quarterly basis to gauge how your support techs are doing and places for improvement possibly with an incentive attached.
2) Instead of asking for support at the closure of every ticket, adding a "feedback" section on your ticketing center (via the web gui) for customers to provide ad-hoc feedback there for tickets WITHOUT getting hounded with emails asking them to do so. Let's be honest, you're probably not going to get much feedback this way, but at least you're not going to also annoy customers.