To me, it seems that moving up from F3 to F1 (i.e. skipping F2, F3000, GP2 or similar) is a red herring. A lot of drivers managed the change because there was real testing in F1 cars at the time. Timed testing was a brutal way to judge whether a driver could handle F1 power and grip. Some teams allegedly made it a maturity test, making the driver wait to the end of a session after others had worn out the tyres.
Drivers with starts in a variety of different classes are more likely to cope with the big step. If a driver has experience in two types of single seater -- driving school car to get a racing licence and F3 -- you can guess whether they are quick but you don't know if they have the other track skills.
Historically, some F3 races (Monaco, Macau) have counted more than others. Partly, that is down to F1 team bosses making time to watch challengers on a tricky circuit.