First of all, civilian GPS receivers only receive the L1 civilian GPS downlink frequency, so they fundamentally get only the precision that comes with L1.
If you had military GPS receivers and could receive L1 and L2 frequencies, you can get much better accuracy. However, you don't have sufficient access, so you can't get a military receiver or the crypto codes to run it right.
Air Force Space Command is trying to spiffy up the newer satellites to have other downlink frequencies as well, with the intention that they can do other snazzy services and stay one step ahead of the EU and Galileo.
Personally, I would not want to have my GPS receiver getting a downlink when it is in a parking garage, because the downlink would be bouncing around terribly to get there, and that is terrible for position accuracy.
I can see a little good out of having more satellites up, but not a lot of good. You already get an overdetermined PVT solution as it is, and the only situation where more satellites would help would be if you were deep in a box canyon. I've had twelve "birds" showing on my receiver, and that is only three times as many as I need.
The receiver's GPS chipsets are getting better because the designers are putting more and more digital correlator circuits in there. That is what is getting you the quick TTFF. They need to design in more heuristics to the receiver user interface.