Why is apparent solar time not used to measure on a clock?
Because, when using "apparent solar time", the length of a
"solar day" varies slightly during the year. (This is because the
Earth's orbit isn't exactly circular and the Earth's axis is
tilted.)
"Clock time" is based on an average (or "mean") of these day
lengths, called the "mean solar day". So clocks use "mean solar
time".
(By coincidence, on the date the question was answered (14th
April) "apparent solar time" and 'clock' time are
synchronised.)
There's another reason for apparent solar time being different
from clock time.
"Clock time" uses time zones. So, over a wide area, the time on
a clock equals the "mean solar time" at a particular, defining,
longitude.