Now as li-ion has been cheaper, more robust, and better in every imaginable way for years already, it would be weird to design anything around the 12V lead-acid voltage anymore. 3s li-ion is close; but neither 12V LA or 3s li-ion matches the ATX spec anyway, so does it matter?
Looking at both simplicity and efficiency, I would like to eliminate all redundant power conversion steps. I bet most 12V PC stuff would work just fine with significantly larger voltage range, as the 12V is just a completely arbitrary voltage and is locally bucked down to several voltages, highest of which tends to be around 5V, and most power is consumed in lowest (around 1V) core supplies.
Of course it would violate the ATX spec, but it could be interesting to try tying a 3s li-ion pack to the "12V" line. The cells would float at 4.00V/cell, which is quite acceptable at around 80% state of charge. At about 20% state-of-charge, the pack would be around 10.3V, which shouldn't pose any actual problems, unless a specific device monitors the input voltage too eagerly, being "too smart" against out-of-spec ATX 12V. This would need to be tested.
Generating the required 5V/3V3 lines would be a walk in the park, as they tend to be low-power lines, and accepting one extra conversion step for them wouldn't be an issue. Most of the power would run with zero extra conversions compared to a non-UPS system.
For this to work, the standard ATX supply would be replaced with one that can support CC operation without faulting, for charging the battery after the outage, and small buck converters added for 5V,3V3 low power supplies. Apart from the battery itself, the cost and complexity is about the same to a bog standard non-UPS ATX supply.
This is basically how laptops internally work. I'm 100% positive something like this is used in some server hardware, as well.