Astronomy commonly uses TAI or raw GPS time. In fact if you look at video footage from NASA control rooms and such there's usually a GPS second clock up on the wall somewhere.
The motivation for leap seconds wasn't astronomers, but to just keep civil time tied to solar time long term. However, the unpredictability of these leap second additions has proven to be pretty annoying, causing bugs and such. This is why google and others actually "smear" the introduction of their leap seconds over half the day.
Considering the current difference is 37 seconds, its natural to wonder if this is worth it. Certainly most people wouldn't notice relative to dawn dusk for a very long time, long enough that the entire concept probably wouldn't even make sense anymore. So why not just stop? That's the basic argument here.
It seems like JPL (NASA) and the scientific community have defined two currently used sets of time standards for observations from Earth and from space near Earth. https://en.wikipedia.org/wiki/Time_standard#Time_standards_f... Barycentric Coordinate Time (TCB) and Geocentric Coordinate Time (TCG) with DE430 as the current revision of their standard https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Deve...
Look at astronomical software, e.g. xephem. There will be a "clocks" tab that displays a number of different clocks, TAI (atomic clock, no leap seconds), UTC (global civil time), media solar time (GMT, which ISN'T UTC) and finally, derived from the aforementioned "sidereal time", which is the one you really need to adjust your telescope. Sidereal time is derived from a year with 1 more day basically, because the earth moving around the sun adds 1 more rotation of the background stars. Which is a drift of roughly 4 minutes per day.
https://en.wikipedia.org/wiki/Sidereal_time
Oh, and then there is stuff like Julian date which you need to look up the myriads of catalogues and tables you need for corrections because everything "wobbles" even more than you'd think.
Yes, dropping leap seconds will remove 1 table lookup from the above. But astronomical time systems are so complex that that change is a drop in the ocean.
For sophisticated astronomy systems the elimination of leap seconds should simplify and reduce a source of errors. As it is, since Circular T is against UTC you need to take your local source of time and worry if leap seconds have been correctly applied (apply leap seconds to gps time or make sure haven't been fed smeared NTP time or other horrors) before you can get UT1.
Fairly casual astronomy, no-- but that isn't driving international standards, and there mechanical uncertainties dominate so you'll end up doing a 1-star correction in any case which immediately corrects the clock.
E.g., suppose you made a system where each satellite transmits messages of the form "Here comes beep #N. At the time of beep #N this satellite is at this position: <X>, <Y>, <Z>. Here is beep <N>: BEEP!".
The satellites are synced so that beep <N> occurs at the same time on all of them.
By looking at the time difference between the arrival of beep <N> from several satellites a receiver could tell the differences between its distances from those satellites. Combined with the position information for those satellites at the time they beeped the receiver would be able to tell its location.
If the satellite broadcasts use a high enough frequency and that frequency is known and very stable the receiver would not even need an accurate stand alone timer. It could sync a counter to the frequency of the satellite radio.