Re: First they came for the leap seconds, then they came for the leap days...
"Solar time where the sun is at its highest above Greenwich exactly at noon every single day."
But, due to the earth's orbit not being circular, the interval between this can vary by +/-O(15 mins). That's why we had to invent a mean day and mean time for practical day-to-day applications. There are just four days in the year when local apparent solar time and mean time are about aligned at Greenwich - as governed by the "equation of time". (Which, I guess, is an example of regularising our time keeping to make computing easier.)
"Every time atomic time goes too far ahead of solar time they insert a leap seconds. So you get a mix of solar time before the decimal point and atomic time to the right of the decimal point."
Yes, UTC is kept within 1 second of UT1. But UT1 is not a measure of solar time: it's a measure of the angle of the earth (the position of the equinox) remembering it takes about 4mins less than 24 hours for the earth to rotate through 360°. Let me quote the Explanatory Supplement to the Astronomical Almanac:
Although it would be possible to define a system of time measurement in terms of the hour angle of the sun, such a system could never be precisely related to sidereal time and could not, therefore, be determined by star transits.
I'm suspecting your 25μs is, anyway, the error in difference between UTC and UT1 (IERS Bulletin B, 12th Feb, gives the mean formal error UT1-UTC as 0.0253ms)
A consequence of this is the mean sun used in GMT isn't even the real mean sun - it's a fictitious one. (Hence the "about aligned" in my opening para.)
I also think it means your assertion that "you get a mix of solar time before the decimal point and atomic time to the right of the decimal point." is incorrect. I get what you're saying; it's not a bad mental model. But UTC is an approximate measure of what you call "solar time" (i.e. the earth's rotation) that is advancing in SI seconds as measured on the "surface" of the earth.
And the point is, as humans, we like that angle. IIRC, the historical record shows 1hr/1000 years is plausible. If the poles disappear quickly, it could get even worse. Nobody is going to accept to sunrise at midday. (Pre-millennial projections over estimate the number of leap seconds we would have. So maybe it will sign flip and go negative; I'm sure negative leap seconds will really piss everybody off even more.) But,drop leap seconds, and we'll either introduce leap hours or time zones shifts, and end up with timezones that are 18hrs off "atomic time". So we'll be saving ourselves some some work in the short term but creating a lot of pain further down the line.