"RE: "It is said Mars moons are easier to reach than iur Moon because of a lower Delta V to get there. And therefore, Mars is also more accessible."

Not really. The argument is that it makes no sense to go to Mars through the Moon for this reason. If your destination of choice is Mars go directly there don't waste time and energy with a detour to the Moon. The Moon is more accessible due to time constraints and it's silly to argue otherwise. What's most accessible on the other hand is of little import. You pick destinations based on what you want to do, not how accessible they are."

I agree completely.
But don't you agree that it's very important to determine whether there is minable water at lunar poles?
And if you don't think it's very important, can explain why?
To help give a full explanation [assuming your argument is that it's not very important]. I shall ask some direct question pertaining to this:

1] Are there any conditions in which is possible that water on the Moon is minable? [And by minable, I mean an enterpise which could be profitable. By profitable I mean that by spending money {investing} one get return on the investment greater than the amount spend- or in other words a real possiblity that such an enterpise is commercially viable. As a further clarification ethanol production in the US is NOT what I mean by a commerically viable enterprise as it is heavily supported by govt money. Whereas companies that make solar energy panels or wind generators, though they did & do recieve some public money in various forms, would be more in direction of "viable commerical enterprises"- though subsidied to a fair degree in "developmental stage" {{ I realize that govt exploration of lunar water could count as a subsidy- and I favor zero tax type policies in regard to Space delevopment which would also be similar to what subsidies solar panel and wind generator received}}].

If you think there is no possiblity that Lunar water could minable, you need to go no further- merely explain this point.

2] Assuming you think there is possiblity of lunar water being minable, what kinds of conditions would at minimum be required. For instance would that there was only at best 1% per volume concentration of water [by which I mean, could be extracted in some "reasonable" mining process].
And at an area size as small as 1 square km scale, what level of concentration is possible- for instance with our current level of knowledge can we rule out chunks of ice at surface or a high concentration of say, 25% water content in first meter of regolith?

3] Regarding demand: Is water or LH or LOX have any value to Manned Mars if these were available at Earth/Moon L-1? Or any L-point or at GEO or even LEO? Assuming it had some value and assuming it was cheap how much per year on average over a 10 year period of a Manned Missions would be needed.

Or let's assume someone is being pigheaded about the need for Mars Direct. Let's assume you are blasting off Earth going to Mars but let's assume you are not going to accelerate the whole way- burn for less than a day or less than a week, whatever. At the point you stop accelerating you are then offered for sale: water or LH or LOX. Any interest these things? Or how about some extra sheilding? A spare module in case the crew needs time alone? Food. Drinks. Dancing girls? Anything?
[If you not accerating then this stuff can be drop off at any distance you think it safest to allow a non-NASA space vehicle to get- 100' or 1 kilometer and it stay pretty much in the general area until some NASA qualified technican retrieves it. If you actually going to allow this non NASA thing to dock to a NASA vehicle then continuous acceleraton isn't a issue.]

4] Mars colonization. Any kind of commerical mining in Space should make colonizing Mars more likely to happen and in shorter time period. For most people colonizing Mars is something which seems fairly distant, but if water was being commercially being mined on the Moon or even instead an asteriod or two, this should change people perception- bring Mars colonization closer to reality. And if this in the case, it seems to more funding for Manned Mars mission would be more likely.