Earlier quoted context omitted.
People who want a predictable and monotonic time scale
SI seconds (in UTC) lead to leap seconds. With UT1, "1/86400 of a day" seconds lead to a predictable and monotonic time scale.
There is no device available that allow you to derive a clock from the relative motion of the sun about the Earth’s axis, such that the changing definition of days and seconds relative to realizable clocks can be tracked.
Furthermore it’s kind of nice to have a stable and standard definition of seconds and days. For instance, under the “ut1 system” you don’t know how long a present second is until the present day’s final observations are made.