I'm guessing you can do so because you can qualify with your own sidearm at the range and demonstrate proficiency. Agency can attest and has documentation based on your range performance you are then "good to go".
The same isn't as doable with a personally owned radio, unless you have a service monitor, have vendor training, access to updated CPS, firmware, and MTNs, can certify it's tuned/aligned, programmed by an authorized person with proper codeplug/template, and especially in the case of used/secondhand/aftermarket radio, no issues exist due to all the backyard TEKNISHUNS with stolen depot software building junk radios from parts. Agency has no real way to vet said radio and the liability is on them if they allow it, something goes bad, it's now on the agency who allowed said radio on the system.
There is much more to a modern radio like an APX and much more than how an Astro 25/P25 trunked radio network operates that are beyond the scope of a hobbyist forum. A radio used by a hobbyist is no big deal if it doesn't work. I'm sure you'd concur with 22 years on the job that you ABSOLUTELY NEED YOUR PORTABLE TO WORK EVERY TIME the same way you need your firearm to fire when you need it. Those who oversee the radio system are responsible if they allow unknown stuff on their network, and they take it seriously. Take it from someone who does it for a living. We aren't trying to be a pain in the ass. We want you to live.
If there aren't enough radios for officers, this is a command staff problem.