If Benny doesn't kill the courier the story still starts in Goodsprings and still has to find his/her way to NV across the same landscape. As there's no loss of memory there's no need to seek out clues how to get there or complete quests to get them but the safe route and the encounters are pretty much the same. Presumably as a loyal and conscientious eager for payment courier you'd be less likely to veer off course and do jobs for other people, so:
- Ringo stays in Goodsprings which gets overrun by PGs
- Trade continues to suffer because of the ant infestation near the outpost.
- No one hears that Nipton has fallen
- Primm still needs a sheriff
- Powder Gangers hold the NCRCF
- The Novac economy continues to suffer from the loss of cattle and scrap shortages.
- Helios is unrepaired and power shortages continue.
- It's still stalemate in Boulder
- Super-mutants continue to head for Black Mountain
- The Legion digs in at Nelson
- Death Claws thrive in the central area.
- Camp Losthope continues to lose hope and supplies.
The overall effect is a diminishing of NCR power, a decline in the wasteland economy as the PGs get bolder and Deathclaws spread. As the NCR weakens, the Legion entrenches and are far better placed when the final battle takes place. There's no bombing run from the Boomers, the BOS is still down their hole and the Remnants are still in retirement, so the only hope of beating the Legion is to enable Mr. House's robots, whether you do that for him or yourself is essentially your only choice.
IMO. Not that I've thought about it much.