It becomes more complicated to translate between system time and civil time, but there are relatively few applications for which you really need to be able to do that conversion — and libraries that handle those cases are complicated already.
But people like to know when they did something based on their own clock. Already that one hour shift causes goddamn headaches in showing the proper time to the user for past events.
Now instead of just figuring out if we're across one threshold or another and adjusting another hour, we have to figure out what time of what day it was and figure out what the offset was at that time?
No. Just get rid of DST.
Deciding there are gradual drifts to standard time on a daily or weekly basis will cause some hassle. But it will not create a new class of problem that doesn't already exist and which doesn't already need to be fixed.
And time is absolutely the kind of problem that needs to be solved with a few standard libraries, rather than every two bit programmer thinking "i can add two hours to this number, it's a piece of cake".