All of that is irrelevant. Like really irrelevant. A.) They make us a seated species to get at the top of the line toys. B.) They don't and settle for buying our top of the line export legal tech in order to remain a relevant power in the face of everyone else who will most certainly be doing that once the war ends. C.) The Turians don't buy from us and everyone else does once the war ends.
There's no scenario where our shipyards lay idle on any significant scale.
I think I see the problem; you are assuming we are going to be selling significant amounts of ships to foreign nations. There are a couple problems with that.
The first is that while things are clearly somewhat different in Mass Effect compared to real life there is a
reason the sale of warships, and honestly a lot of military equipment in general, is the result of deals between
nations not between a nation and a
foreign corporation. We did get away with selling the Zama to the Hanar
but that comes with some important caveats. We showed the Zama off in the same turn as we did the Lite Laser Pynda which is a vastly superior ship for a lower price (41.4 billion vs 36.3 billion). They are also both Frigates which are by far the most common type of starship; to the point the Terminus produces an AK-47 version in the Wuni so exporting them likely isn't viewed the same way as "real warships" aka Light Cruisers and up.
The next is economics. Starships are
expensive as hell. As a point of comparison your basic Gladius fighter, if we sold them, would go for ~350 million. Even the
Wuni Frigate costs 18 billion credits or 51 Gladii fighters and a Zama at 41.4 billion represents 118 Gladii. The Hanar have gone
all in on their military overhaul committing to building the largest military they can economically sustain:
It has been recently announced that the Hanar intend to replace their entire fleet with new vessels and to build up to the largest possible Navy that they can possibly sustain economically. This includes seven brand new Dreadnought class vessels, as well as five to six thousand other combat vessels and numerous additional support craft.
but they are on what is basically a religious crusade. No one else is going to be interested in completely overhauling their navy at the cost of their entire economy.
This all ties in to the biggest problem; militaries exist for a
reason. The Turians have the biggest baddest military in the galaxy because
that is their job. They are the Citadel Council's beatstick intended to defend against unexpected threats and, more commonly, enforce Council edicts on its members by the threat they impose. Outside of them however most navies are for shows of economic might (hence the Destiny Ascension), defense against pirates, and for centuries now a hedge against the Batarian Hegemony and the Terminus. Once the war is over however the last big military threat to the Citadel will be broken. With the Hegemony shattered and the Terminus' fleet likely shredded in their defense who is left in the known galaxy to pose a threat? What danger exists that would drive a massive and expensive overhaul of militaries across the galaxy?
In short why would anyone
care that the Alliance had the most advance navy in the galaxy? They've lived under the
Turians having the largest and (to a lesser degree) most advanced nation in the galaxy for centuries. The Alliance isn't a threat; we're a tiny nation with an
insane amount of space to grow into and a slow reproductive rate that we won't fill that space for centuries to millennia.
So without an immediate and pressing threat driving nations to upgrade I expect most nations will do exactly what the Turians did in response to the Legionary; invest in their own development programs. They can't reverse engineer our technology but its simple existence proves that it is both possible and not outside existing manufacturing capabilities. Sure it might take them decades to create imitations but they have no reason to feel rushed and doing so builds
their nations rather then fueling the expansion of the
Alliance.
Also, even if we don't give them a planet, we already have our own system; just letting them stay there - with the promise that their mining claims and facilities will be respected and not run out of town - would be a major boon.
The Fortuna system was actually an interesting choice in this regard. Amaranthine is uninhabitable (1.16g, -178C, 1.19atm, CO2/N2 atmosphere) but so is Maganlis (1.1g, -150C, 1.03atm, SO2 atmosphere) and they honestly aren't that different in terms of habitability. The temperature needs increasing (Arc Reactors!) and the atmospheric composition isn't breathable but outside that they are fairly close to habitability. Amaranthine is preferable since we can crack the CO2 into O2 and carbon for a Nitrogen/Oxygen mixture that is friendly to humans but while SO2 is harder to work with it isn't so problematic that setting up Arcologies on Maganlis is impractical.
That said I doubt we could offer the Quarians space within our system because while we "own" it it is deep in the Systems Alliance heartland and I doubt they want to be inviting a foreign nation to live there. We are better off grabbing Virmire during, or at the end, of the war since the main problem with colonizing that has always been the threat of raids from the Terminus. The Quarians have the fleet needed to keep it safe, we can build Quarian friendly Arcologies there, and they can alter the biosphere using our Bioforming technology:
[ ] Improved Colonization/Bioforming Genetics Package [800] (Requires Biology Skill Rank B): Increase the speed of safe bioforming and amount of types of worlds that could be changed to be habitable, bringing down the timeline from centuries to mere decades. Would open up much greater range of worlds the package could apply to. (Biotech)
Best of all this mostly deals with this problem:
I'm generally pro-Quarian (read: pro-Tali), but last time there was a general discussion regarding the Mirgant Fleet it was pointed out any discussion about giving things to the Migrant Fleet is really a discussion about directly or indirectly supporting their revanchist policies about Rannoch.
Virmire requires the Migrant Fleet to defend it, Virmire requires resources to bioform, Virmire is an attractive planet to live on. The first keeps them from going on military adventures, the second keeps their resources focused on their new "home", and the last passively wins over the populace to colonization over vengeance.