The Moon is not a useful launch site for projects elsewhere unless a lot of the mass comes from there (ie, lots of fuel or the mission itself).
You lose a lot of dv by stopping mid-trip; this isn’t like pulling off at a rest-stop.
You lose a lot of dv by stopping mid-trip; this isn’t like pulling off at a rest-stop.
I find that quite odd, since there is still so much we don't know about the Moon. If we have the technology, why wouldn't we send someone there to explore and make way for making of a lunar base?
A mission from the surface of Earth would cost ~13 km/s to get that same intercept - so, yes, it’s considerably more expensive. The majority of that is just making earth orbit in the first place (~9 km/s).
The big problem is that the mission on the moon has to come from somewhere. If you can fabricate your mission entirely at your moon base then the numbers above are accurate. However, if you have to ship stuff in from Earth - well, the Earth -> Moon -> Mars trajectory is more like 17-18 km/s. You’ve lost horrendously.
There are certainly perks to things like off-Earth fueling and assembly, but unless you’re getting a lot of the mass from somewhere other than Earth you’d be much better of doing that in low earth orbit (just from a fuel efficiency perspective, and there would of course be lots of other benefits to being so close to home).
If there is anything to pick up from the moon it makes more sense to deliver it to LEO first and continue from there.