all too often a "backup" gun becomes a "throw down" gun
So, how is that when the serial number is recorded when you qualify with it? It will take 15 minutes to go through records and figure out the bad guys gun was one you qualified with for the past 10 years. In 20+ years and numerous case studies from around the country, I have never seen a case in which a "throw down" was part of the case. If that were the case, I would have a "throw down" knife that couldn't be traced. The idea of a "throw down" is Hollywood lore and wive's tales. I'm sure it has happened, but not often enough that it's "a thing".
Unless of course you carry a file in your pocket and stand around at the shooting scene filing on the "bad guy's gun". And the FBI allows a BUG, and have for years (Miami shootout in 1985 they were there), the DEA allows a BUG, and the ATF actually ISSUE a BUG from a list the agent can choose from (at least this was case a couple of years ago).
I only PERSONALLY know of 1 department that forbids them, and that's a local department in my area that's more of a group of night watchmen than a police department and are the laughing stock of the area anyway.
As far as cost, I understand the budget constraints, but I don't advocate the department issuing guns and requiring a certain gun to be carried anyway for the reasons mentioned above. In that case, money plays no role to the agency as far as how much a particular gun costs anyway, except for the PIA of ordering ammo in 4 or 5 different calibers instead of 1.