I recommend using as little as date/day mechanics as you can get away with. Instead using a monotonic durations as much as you can [1].
If you continue to program with date/day mechanics you'll run into plenty of issues when users cross timezones or just set the time on their phone to a different one.
My favorite things is when you connect to cell towers that have DST in one state, and not in another, the cell phone getting the time/date from "the network".
Yes, getting rid of the various savings time is important too.
All the people pointing out the (genuine) problems with decimal time seem to be weirdly tolerant of the problems with our current system, which has much worse problems.
If you imagine the reverse situation, where society uses a decimal time, and some people are arguing we should switch to this system because despite all the things it makes worse and harder, it divides better and the numbers map somewhat (although imperfectly) to the actual time-of-day in various locales and (even less perfectly) to the kinds of things people might be doing at that time, everyone would think they were crazy.
Firstly the time variance we're talking about is small and will only matter when milliseconds matter, secondly I addressed this - for scientific measures and scenarios where milliseconds matter a different time unit should be used.
If you want to prioritise ease of moving between the two systems, I'd suggest a normalised version of the new second. If you want to prioritise science, then something that makes a nice round number when giving the speed of light would be nice. If you want to prioritise ease of adoption, just keep the current SI second, just stop using it to measure times of day.
Either way the symbol for writing it should be different.
Of course, computers and humans must use the same time system. Which is why now that we have computers, we always specify the number of milliseconds in everything. Unfortunately, until someone builds a type of computer that can do the type of math needed to convert between two measurement systems, this problem will remain an insurmountable obstacle.
This is reasonable and not unsafe at all, particularly when it comes to timing things like exposure time with patients receiving radiation therapy.
However, we will be left wondering why treatment in the summer is more effective that treatment in the winter. Must be the nice weather.