I've never chosen the City Watch background, but I could imagine a lot of reasons to play a "cop."
Even if your group is all diehard ACAB enthusiasts, trying to do the right thing by protecting the city while also rooting out corruption in the force could be a very rewarding campaign. Heck, there are entire movies and TV shows built around that premise.
Beyond that, I could also see being a member of a City Watch for a new settlement on a hostile frontier being potentially fun in a lot of different ways. You could be part of managing the success of a new settlement. Note that a "city watch" needn't be in what we think of as a city; a wood elf outpost or druidic enclave would likely have just as much reason to have security as an urbanized metropolitan area.
As mentioned above, there are plenty of movies and shows from which to take inspiration. Something more silly could be a fantasy version of Super Troopers, Police Academy, or 21 Jump Street; going the 80s action movie route could be inspired by Lethal Weapon or Miami Vice; investigative adventures could be like Law & Order; and etc.
Thinking more... I could see a whole campaign centered around being run-of-the-mill City Watch members for Sigil. Maybe one week you're investigating an illegal drug ring believed to be run by a group of rogue celestials. Then maybe that leads into uncovering information which unfolds into a much larger story arc. Perhaps it's revealed that the specific substance is part of a plot to drug the Lady of Pain and weaken her power so that someone else might attempt taking her place.
plenty of directions that background could play into a game of D&D.
With a few tweaks, you could also use the background to create analogs to EMTs, firefighters, and various other things that a city might need.