The main reason was to make it easier to market these flights. Back in the good old days, when most people booked tickets via travel agent, such flights with 1 flight number would show up top of the list of possible flights, even through it wasn't really non-stop (just "direct" as they called it). This is still true today--most airline web sites can show flights in order of stops required.

Also it allow the airlines to offer fewer miles to the flyer, since they count these flights as one "flight", despite having to change plane type and gates. On the other hand with some airlines (like UA?), it's possible to get upgrade for the whole "flight" with fewer upgrade certificates than otherwise, if the flights has been counted as 2 separate flights.