The answer is cost. We used to have the computers you're describing. They were made by SGI and the hardware & OS made all sorts of guarantees like the ones you're describing, to the point where XFS was ported to Linux x86 initially it had all sorts of bugs that simply couldn't happen on SGI machines.
The x86 boxes were cheaper, nobody really cared enough about hardware reliability enough to pay the price for the likes of SGI, and the rest is history. Today we have a "worse is better" hardware architecture and software has to be able to handle it.
[1] http://www.mouser.com/ds/2/257/Maxwell_HCSeries_DS_1013793-9...
The 10 F capacitor has an ESR of 0.075 ohm, but that's at 1 A. They have a 100 F model that is 0.015 ohm at 10 A, and a 150 F that is 0.015 at 15 A. Based on your calculations, these look like they would have a good chance of giving enough time to save everything (especially on an SSD system).
Those are physically bigger but should still fit in a normal desktop or server.
(There is another manufacturer that has up to 630 F!)
Adding $20-50 in bom the size of two D batteries just in case something _very rare_ happens is not economically viable. There are better alternatives, like banks of batteries ala google boxes. Turning server into oversized laptop gives you more than couple of seconds buffer.
1. The PSU would have a big enough capacitor to keep the computer running for a few seconds at its stated output power
2. The PSU would notify the OS of a power loss
3. The OS would immediately flush all caches and adopt a "brace position".
4. Events are spread system wide so that apps can also flush and brace.
It should work even if it is the PSU that fails (as long as the capacitor is there).
Surely the problem cannot be the cost. Why don't modern desktops have that feature?