Very easy answer: Because it's already painful twice a year, and that would be making it even worse.
That answer is similar to the one for questions like "why do we have wide time zones that are somewhat inaccurate, rather than setting every clock based on the exact position of that clock?".
While this feels would be a disaster for other reasons like: “How many seconds are in an hour?” -> “Depends, no one knows.” … that’s already the case with our existing leap seconds.
Which we are also in the process of getting rid of.
(This sounds like kicking the can down the road to me; making the maximum discrepancy a minute could take 50-100 years and then you need a leap-minute or equivalent).
If we move to leap-minutes, the Earth will do whatever it does, and it is expected that we'll be able to run on atomic time for a period of decades or perhaps even a century before we need to make another adjustment like we've done with leap seconds in the past.
https://en.wikipedia.org/wiki/Leap_second#Phase-out_and_futu...
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edit: Yeah, I see that your edit covered this adequately. No worries. :)
To that end, I'd like to propose 12 transitions. These should happen on the 16th day of every month, at precisely 05:14:33.
Let's take our seasonality more seriously.