To the best of my knowledge, these days, there aren't really that many "direct" flights in the traditional sense, with one or more stops at hubs while keping the same flight number (like LGA-DFW-SFO or something like that). That concept of the "direct/through" flight seems to have gone away in the past decade or so. (Incidentally, I remember we used to complain on this forum back in the early 2000s that if you happened to book your ticket as a "direct" flight such as LGA-DFW-SFO with a single ticket number, you would earn miles as if it were a nonstop LGA-SFO instead of for each segment.)

Nowadays, each unique flight segment has its own number. So you could still book LGA-DFW-SFO, but LGA-DFW would be one flight number, and DFW-SFO would be another. I suspect it is because everyone has to deplane after a flight anyway for aircraft cleaning/catering/security checks. Even if, by chance, one's connecting flight happened to be operated on the same equipment as the inbound flight to the hub (which is highly unlikely at a massive station such as DFW), you could not remain on board in between segments like in the old days.

The one exception to what I wrote about is rather interesting. AA has started using the same flight numbers for quick turns to smaller outstations, such as in the Caribbean (and possibly Midwest too), where an aircraft goes out and back on the same day. (MIA-BGI-MIA is all the same flight number, MIA-AUA-MIA, etc.)