Depending on how late the go-around/aborted landing is triggered, that can be a danger in itself. Any unexpected event in the landing flow has a risk, to the point that there's a "sterile cockpit" rule in that window.
Even if it's just a warning to the ATC, distracting them and forcing them to reexamine a false positive call interrupts their flow and airspace awareness. I get what you're saying, that we could err on the side of alert first, out of precaution; but all our proposed solutions would really come down to just how good the false positive and false negative rates are.
BTW, stopping at a red light unnecessarily (or by extension, gunning it to get through a yellow/red light) could get you rear ended or cause a collision. Hard breaking and hard acceleration events are both penalized by insurance driver trackers because of that.
I'm assuming there that any such system would be appropriately tuned not to alert outside of a reasonably safe window. My assumption is that it would promptly notice the conflict following any communication which under ordinary circumstances should leave plenty of time to correct. To be fair I don't expect such a system would address what happened in this case because as you note false alarms on too short a notice pose their own danger which may well prove worse on the whole.
This specific situation I think could instead have been cheaply and easily avoided if the ground vehicle had been carrying a GPS enabled appliance that ingested ADS-B data and displayed for the driver any predicted trajectories in the vicinity that were near the ground. Basically a panel in the vehicle showing where any nearby ADS-B equipped planes were expected to be within the next 30 seconds or so.
> stopping at a red light unnecessarily
Is it not always legally necessary where you live? It certainly is here. When I described them as unnecessary I was recalling situations that would clearly be better served by a flashing yellow.