When I was in Cochise County (in AZ) the SO had one deputy that was trained to dive - that was their "team" then. I volunteered, as they had a process to apply. Seemed that they just went up to other LE offices rather than maintain a volunteer team. When it comes to recovery, that's not an issue. But if you're talking immediate response, southern Cochise County is quite a ways from the closest major city. Things might have changed, but that's the way it was in the 90's.
A friend of mine was a serious caver, who volunteered with the county also. She was called on to assist in a situation, but only because she was also on the volunteer roster an hour away in Tucson as well. She got called in as part of that team.
In NE Texas, the county team embraced my offer. They employed my skills where they could, and didn't involve me in aspects that weren't appropriate. Given that their diving experience was somewhat varied with some of them being very new, this was a very good approach, IMHO.
I do understand legal implications involved here, but the risks can be mitigated IF the agency looks for potential talent BEFORE an incident, and begins the process of establishing an augmenting force to their full-time crew.