That ephemeris data is good for 2-4 hours, so one simple technique to improve lock times is to save it, and then if you turn the receiver back on within that window, you can reacquire a lock almost instantly using the saved ephemeris data.
Another technique is to download the ephemeris data from a source that can provide it more quickly, such as the cell network. This skips that long transmission at 50bps from the satellites themselves. Pretty much any GPS chip in a cell phone these days will do this. This is called assisted GPS, or A-GPS. (This is not to be confused with another technique also called A-GPS, where the GPS chip captures the signal and sends it to the cell tower to offload the computation. This was a popular approach in older phones to comply with 911 reporting requirements, but doing the computations onboard is cheap now.)
Starting with a coarse guess of your location can also help shorten the time to initial lock, although it should be fairly short regardless. That guess can come from looking at cell signals along with known cell tower locations, and a rough altitude estimate can be made from the device's barometer.
All of which is to say, getting a dot almost instantly when you turn on location services doesn't necessarily mean too much here.
It could be tricky to do securely. How do you prevent a malicious device from spoofing bad location data?
Android and iOS do something sort of like this already, determining position by looking WiFi base stations with known locations and attempting to do some triangulation. This can speed up a fix if the GPS signal is having trouble, and can be essential for indoor location because GPS signals don't penetrate structures well at all. My understanding is that the database gets built up by the devices. When they have a good location fix, they'll report back on the WiFi base stations they see, so that the mothership can build a database of where the things are. This is a little bit like what you describe, but with a really roundabout data path.