GPS antennas typically need power. GPS receivers expect to be the sole power supplier. Simple, cheap signal distribution won't handle this. There are splitters that can allow one downstream port to supply power, but that fails when that single receiver fails. There are other splitters that are active-active. I guess you're claiming that the boxes from Time Machines are such active-active devices.

Those are not cheaper than an antenna! Although from the photo I'm not sure he bought the cheap antennas.

Speaking from experience deploying stratum-1. Not stratum-0, but the same GPS concerns.