Al_ said:
Fair enough, I should have been more cautious.
How about this: It seems to me that getting fuel from the Moon is a smarter way to proceed, and the problems of mining seem soluble.
Smarter than launching from Earth? For what mission? That's what the problem here is: you're speculating wildly about missions that aren't on any kind of time horizon. It's been said that anything 30+ years away is essentialy "never" for planning purposes. But what you are speculating toward is likely hundreds of years away. Backing-up:
Ok, so the OP asked: "Would it not make sense to launch [to Mars] from a base on the moon [instead of Earth]?"
The OP did not state for what purpose one would be going to Mars, which left members to speculate. You can see how this can lead to wild hypothetical mission plans, I'm sure: Perhaps we need to amass an invasion force to attack the Galactic Empire's Death Star factory on Mars? How should we fuel it?
Here's the chronological reality:
1. Humans have never visited Mars and we don't yet know what even the first exploratory missions will look like. We *might* make such a visit within the next few decades. It seems fairly obvious that for individual (one? ten?) exploratory missions, the cost of building infrastructure on the Moon to assist those missions would swamp the cost of the mission.
2. After a successful exploratory mission, then "we" can decide what the next step is. For the moon, it was a 50 year and counting pullback. Perhaps it will be for Mars too.
3. 50-100 years from now, after our successful exploration program ends and we take however long to re-assess the next step, Elon Musk and Donald Trump are dead and assuming SpaceX and the USA still exist, whomever is running them can look into the merits of colonizing the moon or Mars. But even then, such an effort would almost certainly start with decades of small test colonies of dozens or hundreds of people. Probably still not large enough for an infrastructure on the moon to be of help. But maybe. We'll probably have really good robots by then!
4. Then, 100-150++ years from now, if colonization has demonstrated to be doable and there is a need for it, people might start real colonization. And then perhaps a low-g fuel depot on the moon or an asteroid might be worth pursuing.
tl;dr: There is no large-scale fuel need on the forseeable future time horizon (our lifetimes) and speculation about that need, if it ever even happens, is fairly pointless. So for the forseeable future, the idea of a lunar launch site/fuel station is not viable. But it is reasonable to believe that there is a break-even point of scale somewhere -- but let's not let our minds wander too much into what that might look like.