This is actually how all gps devices still work, including the latest smartphones and watches. It's just that now, devices can pre-download the almanac over your data connection, mostly eliminating that delay.

Well most offline devices don't take minutes now except for the first fix in a long time. It's generally around 30 seconds to a minute.

Usually the almanac is stored in non-volatile memory so additional startup fixes are much faster.

It's more than that too, old receivers couldn't track and download from as many satellites at once. All modern receivers can pull almanac/ephemeris data from pretty much everything they see at once now.

I've got an eMap - last time I tried it (after it was off for N years), it took upwards of 20 minutes to get a fix with a clear sky because it could only track (AFAIK) 6 satellites and without the hints from recent use, it struggled badly.