That makes sense, but how much does the delta-V requirements change from best case scenario to worst case scenario?
It depends, but probably not much in most cases. For the asteroid for example, you can see from the map that you need 664 m/s to raise your apogee to the Moon level, and 17 m/s more to reach the Earth's SOI limit, so 681 m/s. The asteroid is between those, so both best case and worst case are in this range (664 to 681 m/s).
The most worrying situation would be a transfer from Earth to Mercury: Mercury's orbit is noticeably elliptic, and the difference would be much more. I made those calculations once, depending on whether Mercury is at the perihelion or the aphelion:
The final results is in the lower part, the rest is intermediate calculations.
You can see that there's more than 500 m/s between both situations. It could also be confusing because the best case (when Mercury is at the perihelion) corresponds to when Mercury is the farthest from Earth, so the transfer from Earth is the most expensive. Then the insertion around Mercury is the cheapest, so overall it's better, but without clear indication about it I'm pretty sure that 99% would get it wrong.
That's the main problem, even if just giving the worst estimate would guarantee your success.