0. Human diurnal local time
1. Universal time similar to 0. but without local offsets - UTC (UT1)
2. Universal monotonic time (within comparable gravitational reference zones) - TAI
These already exist. There is nothing to add or remove, but to do things differently that have already been recommended rather than sticking with insane traditions for another 25 years wherever possible. UTC (UTn), GMT, are insane for timestampping.
Use TAI essentially everywhere and calculate it later as UT1 or local time. If you fail to do so, you risk discontinuities and security vulnerabilities. This is why you should and must use TAI64[N[A]] rather than UTC because UTC is not monotonic. You can get UT1 from TAI by downloading LS tables and doing the math yourself. It is rare to find UTC-centric code implemented correctly.
This isn't rocket science, it's first principles of recording data that doesn't vary nondeterministically in forward time.