The fatal flaw is a standard UPS you'd be lucky to get 15 minutes backup time.
That's plenty for my NAS so it has time to safely shut down, not really ideal for broadband.
There's also the bonus to the "if one component fails, the others still work". For example if all four of your modems have their own UPS each, if one of those UPS fails you still have connectivity. Granted its moot if the Firebrick loses power.
There's nothing to stop you having BOTH though. I have the NAS, router, core switch and 4G router into the UPS. But the 4G router also has an additional 12V UPS, so when everything else goes down I can still connect to that directly over WiFi as a backup. The DSL modems have no backup power as I have no adapter to fit the HH5A, but in a power cut its likely the cabinet will go down anyway. Course the cell tower might too, but likely has more backup power (though not sure if data remains active on backup power).
That's kinda the advantage with ADSL, as its all the way back to the exchange theres a good chance a local power cut wont impact the exchange too, plus it has better backups than cabinets/cell towers.
I also have another 12V UPS running the 12V LED tape in the hall, as emergency lighting. That I believe can run for several hours. I also have USB power banks and little USB LED lights that would run for longer.