True, it's easier to get to NEOs than the surface of the Moon.

Easier in terms of energy.....NOT in TIME!!!
Robots don't care, humans do!

A longer manned flight (away from Earth's radiation belt) means:

1) Taking much much more life support systems (water, oxygen, food, clothes)...

2) Reinforcing the hull against solar and cosmic radiations.

3) Providing more room for comfort.

4) Introducing means to fight against the effects of long exposure to weightlessness.

1, 2, 3 and 4 cumulate and considerably increase the spacecraft's mass, increasing the energy needed, and wouldn't that make the energy saved by going to a NEO rather moot ?

Also, a longer manned flight means:
Psychological issues appearing, weightlessness effects, boredom within the crew and within the taxpaying public, unexpected (as undetectable before a certain time has passed) effects such as moisture, corrosion, leaks.

And a NEO would mean say a 6 months long flight with a NEO visit lasting less than a week!!! Is that an acceptable ratio? A better ratio means more fuel, of course!

I don't by the merit of longer missions, if it's to avoid having to use less fuel.