Alert fatigue is a big problem for any alerting system, but here the baseline is 911 reports. If they receive a 911 report for a shooting, they're going to arrive after the report. If they receive a ShotSpotter alert before a 911 report for the same incident, then they're probably going to arrive as soon or sooner than they would have otherwise. If they receive an alert but don't receive a 911 report, then any response time will be faster than no response.
Not sure if these are backed by data, but there are many quotes of law enforcement saying response times are decreased. I could paste a bunch of quotes but I know it doesn't really mean much.
This study used "gunshot victim prehospital time" as a proxy; arguably a more important proxy:
>Use of ShotSpotter detection technology decreases prehospital time for patients sustaining gunshot wounds - https://pubmed.ncbi.nlm.nih.gov/31425474/
Some other studies indeed found it did not seem to decrease response time, though.
Another factor is that it tries to precisely locate the source of the shot. It's hard for humans to infer the location and direction of a supersonic bullet's source if they're going just by hearing and didn't see the incident, while in theory an automated system could determine it more accurately. I don't know how helpful this is empirically, though.
So you may be right. I think most of the value probably comes from cases where they otherwise wouldn't have received a 911 report, or only would have received one much later.