We could call them lauds, prime, terce, sext, none, vespers and compline.

Fun fact: noon comes from “nona hora” (ninth hour), which actually was mid-afternoon.

how does that make anything easier or better? Every locality will still have a "morning" designation, so when you schedule a meeting with your coworker across the country, you still need to look up his "morning" time so you don't schedule it before he gets to work.

The Japanese came up with such a 'temporal hour system'. An ingenious clock to display time that changes with the seasons is this Myriad Year Clock built in 1851

https://youtu.be/1moRfIXCfak?t=886

What? No really, time with numbers seems to work just fine.