What matters is signal to noise ratio. There is not really background noise in UHF and up; instead there is thermal noise in the receive amplifier.
If you have SNR of 6dB over some integration interval which gave you acceptable results, and you have 40dB of additional path loss, you're now -34dB, and you need to make that up. There's no "taking half" because we're talking about only a 100x difference in receive voltage.
Put another way, we already "took half"-- our SNR of 6dB (quadruple the power) was already only double the voltage. Our metrics for SNR already take what you're talking about into account.
Dynamic range can be a factor, but you generally have some kind of automatic gain control that increases effective dynamic range (so that in absence of signal, you have noise much bigger than 1LSB showing up at the converter), and the conversion dynamic range "width" of the converter only matters when there are other in-band transmitters around you need to reject (because they limit how far you can turn up the initial gain before saturating the converter).
Note also, not that it relates to what we said at all-- you can detect signals much smaller than 1LSB because of dither.