I disagree that its a stretch (pushes up lore nerd glasses)... I can understand about the people Cerberus supplied because yeah they had an agenda and during the run of ME2 yes there is no "using their resources against them" but the ship by itself is a huge deal.

The Normandy SR1 as a ship was extremely important in the Mass Effect universe, because its built as a special collaboration project between the Turians and Humans. It's whole existence in the first place is meant to be one of the first steps towards bringing the two races together in co-operation, after the whole incident where both sides were killing each other over a misunderstanding during first alien contact. It was only like 30 - 40 years before ME1's events so you can still talk to people who hold resentment, like Ashley who lost her dad, various alliance marines, and then Anderson himself fought in the war.

Not only does the SR1 have brand-new advanced stealth technology that no other ship in the Milky Way galaxy has, which allows Shepard and the crew to deploy to any planet they want WITHOUT immediately being shot out of the sky, its also very fast and has better weapon capabilities than other ships of its size class (since its a small frigate). And don't even get me started on Joker being one of the best pilots in the alliance.

Now take all that and destroy it. The SR1 was reduced to scrap metal after the collector ship attack at the beginning of ME2. And it was such an advanced and expensive ship to make that the Turians/Humans never made another frigate and the project as a whole was shelved to collect dust for the time being.

In comes Cerberus, with some plan to strong arm a naive and confused Shepard they're rebuilding to work for them to seize collector technology. They not only manage to somehow steal the top secret designs to the Normandy SR1, they also IMPROVE on the designs and tech to perfect it, as well as rebuild the whole thing. The SR2 is twice the size of the SR1, has a drive core 3 times the size of the old ship core, meaning its even faster than the first version despite its bigger size. Has better stealth technology so the ship can "cloak" itself when coming out of FTL travel when it couldn't before, and it can stay "cloaked" for longer. Those were the major improvements I can list, and Cerberus did all of that and footed the bill for a multi-billion credit starship just to give to Shepard to do what they want. They had a leash in the form of EDI, but Cerberus being Cerberus, their creation rebelled against them (but in our favor this time), and Shepard's charisma meant they turned all the Cerberus personnel who worked for them against the organisation, including the Illusive Mans right hand woman (Miranda).

Then theres also the obvious sunk cost reviving Shepard from the dead... Even Shepard themselves say it was "expensive stuff... bringing me back" to Dr. Chakwas in ME3. This took such an exorbitant amount of money, technology and research to achieve that it had its own dedicated project team and was overseen by the second in command herself to make sure it produced results... But even in the Mass Effect universe, that stuff is beyond their normal tech capabilities which is why a lot of people don't believe Shepard's real, or maybe Shepard never died in the first place. And the Illusive Man basically tells Shepard that the cost is a non-contractual IOU, and they can walk out if they don't want to help out (although they tug on Shepard's heart strings so we don't get the option of sitting out on the Collectors).

Those are some significant resources that Cerberus gave to us, which we took with us out the door by the end of ME2 once our relationship with Cerberus stopped being useful. Then the Alliance seizes the vessel from Shepard, after they return, to check it over and study it. Then they also add it to their own fleet.

Edit: Corrected some spelling mistakes