The fact is that the GPS satellite clocks DO include a frequency adjustment to account for the effects of relativity:
"Therefore, on balance, the clocks in the GPS satellites in space appear to run faster by about 38 microseconds a day than the clocks in GPS receivers on earth. So, to ensure the clocks in the satellites will actually produce the correct fundamental frequency of 10.23 MHz in space, their frequencies are set to 10.22999999543 MHz before they are launched into space.")
Furthermore, any signal from the earth is subject to unpredictable delays due to atmospheric effects (see https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Atmospheric_effects). That would complicate using a signal from ground to synchronize GPS clocks.
How the time signals from the ground are currently used in the presence of already corrected clocks is not a reliable indicator of how well they would work without the relativity corrections. Anyone who proposes that the relativity corrections are not necessary would have to do a lot of detailed, expert work to back that up. I don't see any convincing evidence of that sort.
So what? Surely there is 38 microseconds time dilation shift per day and it is corrected by frequency modulation. I have written the same too.