For example,was there any sort of metric system proposed for time where there were 25 hours in a day, with 50 minutes per hour/seconds per minute?
Indeed there was. During the French revolutionary period a new calendar was introduced with 12 30 day months each with 3 10 day weeks. This worked quite well, and was really only abolished by the restoration of the monarchy who wanted to change everything back to how it was before 1789.
It was complemented by a decimal time system with each day divided into 10 hours and each hour into 100 minutes. Each day would therefore have 1000 minutes rather than the 1440 minutes we are now used to.
Sadly it didn’t catch on, presumably because people were very used to the time system they already used and an established infrastructure of public clocks.