True, they would initially be the first to place and maybe get a chance to mine the ores before being flagged for termination, however how long they would mine the moon depends on the probers of bigger alliances willing to find that exact moon and the exact goo they seek. Might be a day, might be 3 months before the athanor gets popped.
Right now, a smaller alliance has the only income from taxation of their members. Wherever they try to raise structures to add an additional income parameter, and I mean of any type, not just moon goo, bigger lads come in and stomp them.
It is what it is, I suppose, you build a sand castle and someone tears it down 
However the smaller guy should have some other way to diminish their losses and not just opt for a way out by joining one of the bigger alliances, either as corp into alliance or via rent or via blue status, which will eventually end up being what it is today, a big blue donut on 2 or 3 sides. Right now, I think, its Goons + blues vs Frat/PH + blues vs Fire + blues, the others aint worth the mention cause as soon as they start working on their own, guess what happens: ROFLSTOMP!!! And not because they are a menace, but lack of content for the cap pilots (which is a story of its own which I will not get into now).
So basically if you discover a moon with lets say, cadmium or some other more expensive stuff, like tech/dyspro etc., from moment of scanning, you would be able to see how much more ore is left on that moon and decide on whether to mine it or not. Should be coded in as a sizeable amount so its worth the time and the ships frontlined to fight for it. Once you mine the moon goo out, the moon is depleted and you have to search for new mining grounds. This wont mean its a dead moon, but at some point down the line, the moon will respawn a different set of moon goo materials ( NEW RESOURCES DISCOVERED!!! 
) and then you mine it again. Who knows when or what type of goo is viable for next mining run. A random cycle of lets say 7-21 days would be the interval between the moon goo respawns. Also the rates of finding these new mining grounds and location should also be randomized so you would get R64 in both low sec and null sec areas, but more often in 0.0 then in low sec. Still moon location would be random and not locked to a region.
I dunno, but I think this would also be a viable option for WH moons too, giving the small alliance / corp the chance to rebuild their stockpiles / fleets faster and provide them options to enter bigger fights without worry of going bankrupt due to heavy losses which they cannot come back from.
I reckon it would be a massive struggle to code this into the game, but maybe in the long run, it does provide an equilibrium cause right now, same as in RL, you got the poor ■■■■■■■ and the rich ■■■■■■■… There aint no middle class corps / alliances.