The biggest pro is controlling/eliminating ICH outbreaks. Regardless of how you QT and what you do, stay in the hobby long enough, add enough fish and you will eventually most likely have an ich outbreak. When you do, it can easily cost you all of your livestock. Think about that for a second.... Every Last Fish... Dead...
UV downsides:
Most of these are REALLY reaching out because they're not a big downside at all and are very very minor.
* Initial cost. They can be expensive to buy a decent (Emperor) UV.
* Additional electricity. Maybe $2/mo? dunno.
* Annual bulb replacement. Less than $100?
* Pod kill-off? Sure, it'll kill whatever free-floating pods go through it. However, pods aren't generally in the open water column. They are in the rock, substrate, algae.
* Additional heat source for the tank. Again, very very minor if even noticeable
And that's about it that I can remotely think of for downsides. There are virtually NO downsides to running a UV other than the initial cost. However, as the saying goes, an ounce of prevention is worth a pound of cure. Kill $1k in fish and then tell me you "can't afford" a $400 UV setup.