If the first active component is an amplifier than it IS the pre-amp, and its noise figure sets the noise figure for the entire receiver.
Ok, you are right. It is the first amp in the system so I guess you could call it a preamp. As all active devices generate noise, it does contribute to the overall noise in the system. But when most people think of a preamp they think of an amplifier that deals with very weak signals (<0.5 uv) and boast that weak signal up to a level strong enough so your scanner can detect it. Drop Amps don't work that way, they take a fairly strong signal off the air (>100 uv) or a very strong signal from a cable TV system (>10000 uv) and split it to feed many receivers while isolating them from each other.
There is nothing magic about setting the through gain to 0 except in cable distribution systems.
But that is the job of a Drop Amp. I fail to see why you think a system gain of 0 means anything more than the fact that the amp has just enough gain to offset the splitter loss. Also, what is magical about cable systems?
If the signal is strong you don't need an amp, just split the signal.
Ever hear of birdies? Spurious signals generated by digital electronics? You need to isolate two or more receivers so they don't interfere with each other. The port isolation of a Drop Amp does this, weak signal or not.
My guess is most people who like these things either switch from a bad set up, or never tried a GOOD passive splitter.
The discussion here isn't that a Drop Amp is the answer to a maiden's prayers but it is a solution to a problem caused by the combination of today's electronics and yesterday's splitters. Will a splitter work? Yes, but so will putting a T in the antenna feed and running both scanners from the same line. A Drop Amp is a good solution to their problem.