There are several issues that surround the army use of the YT-1300(p) Corellian Freighter like the Millennium Falcon (MF), many of which have already been mentioned, but I'd like to examplify a few more. This answer will focus mainly on canon, since that's what the movies rely on too.
The Millennium Falcon is, like many YT-1300 Freighters, a personally modified model. YT's were popular for their 'revolutionary' modular capabilities. It would be impossible to trace what modifications the ship has gone through over the many years to reproduce it in mass;
- (1a) Another issue is that the MF has been completely destroyed and rebuilt at least once, making it arguable if it's even the same ship anymore.
The MF is unreliable, as examplified many times by the movies. Imagine the hell rebel engineers would go through as this ship just gets introduced. Additionally, who would even be able to memorize all the upkeep to each little modified part? Simply, this ship would be near impossible to maintain for a war-waging group, especially in a fleet;
The YT-1300 design is rather old and deemed outdated by the producer, Corellian Engineering Corporation (deprecated around 0 BBY). This would mean getting new parts and the desired (standard) modifications the MF has to be really hard, if not impossible. An army can't use sparsity, it simply drives up the price and makes material input unreliable. Then one still has to consider all the non-standard, possibly self-made modifications on the ship.
Time. It takes time to introduce any new vehicle, tool or any other standardisation to an army. Yes, the Rebels are into guerrilla tactics, but they still standardize too, they have to, after all. You cannot lead an army of troops without instructing them, training them and letting them get familiar with their tools. The Rebel alliance simply didn't have the time (nor the credits) to standardize such a time sink of a ship, with all the factors made in prior points.
One might go now: "Well, how about a standard YT-1300p/f?". These ships were not crazy amazing when they came out. Legends details that the ship did come with great equipment when bought new, for the price, but it was still a freighter, not a fighter. Additionally, try to get a new or intact used YT-1300 after 0 BBY: production was stopped and all used YT's probably already have several modifications on them.
The gist of the whole story comes down to: Standardization. This ship simply is not fit for that as of the time of the Rebel Alliance, due to the feature that made it so desirable: its modularity. Training crew for such a bulky, odd ship (let alone maintaining it) would be hard as well, especially for a more guerrilla focused Rebel Alliance. Why not buy a few X-Wings, Y-Wings or other such ships instead, then? At least those are known by the crew, and they are all reliable enough as well, without many complications.
One last point I'd love to make is that Star Wars does lean more on the fiction side of Sci-fi. Plot armor is a recurring term used, and it is sadly present in SW, if you hate such factors. Han, like many others, simply does get out of situations with the MF when he really shouldn't, simply because the story needs him and he shouldn't die (or any characters that flew the MF later).
Information pulled from the Star Wars wikia page on the YT-1300 light freighter as well as the movies themselves.