Air carrier Captain reported a conflict as an aircraft was cleared for takeoff on the same runway while they were on final approach below 500 AFE resulting in a go-around.

Narrative

While conducting the visual approach backed up by the ILS 35 ILM; the aircraft was fully configured with landing checklist completed. I was pilot monitoring (PM); and the First Officer (FO) was pilot flying (PF). We were below 500 AFE; and the Tower cleared an Aircraft Y to takeoff on Runway 35; and the aircraft was not even in position on the runway; they still needed to line up. Aircraft Y was instructed to expedite with no delay to begin their takeoff roll. Aircraft Y could only go so fast; and we quickly saw this potential disaster unfolding. The FO keyed his microphone and said 'this isn't going to work'. Moments later at 396 AFE; the FO initiated a go-around at his discretion. Tower said 'let's wait and see' in regards to needing to go-around. It was blatantly obvious there was zero chance this was going to work. The Tower then directed an immediate left turn on the go-around as Aircraft Y was now climbing into us. TCAS then provided multiple 'TRAFFIC TRAFFIC' TAs as Aircraft Y was right below us despite us turning left. In the process of the GA; the FO did momentarily overspeed the flaps by 1-2 kts. We then were vectored back around and landed uneventfully the second time. The Tower apologized and I requested a phone number to discuss with the controller on the ground after as this was completely unacceptable and an unsafe thing the controller did for seemingly no reason. The Tower said upon the phone call that 'it would have worked out in a perfect world' which was extremely concerning to hear them say this. This isn't a perfect world and in no world would this have worked out.Cause: The cause of this event was the controller clearing an aircraft to takeoff as we were very short final at below 400 feet. This was an extremely poor decision by ATC that should not have occurred. There was also simply no reason for this given it was not busy at the airport. This led to an unnecessary go-around and further complications such as overspeeding the flaps; and numerous passengers throwing up everywhere and being on edge about what was going on.Suggestions: ATC should not have cleared another aircraft for takeoff that close in. They seem to now be aware after my phone call with them that this was not okay and should not have happened. There's not many further suggestions I could make aside from being vigilant of other traffic nearby when landing and taking off so you're aware of potentially hazardous situations such as this.