And here in lies the problem, each Great House has the capacity to make a brand new mech from scratch, and to make pretty well as many of them as they want. It's no longer lostech, the technology is well known, just for some reason everyone is reluctant to build it. Why would you ever build a factory to make a tank from purely indigenous parts if you are only going to churn out 20 odd a year? That should be 20 a day!
The issue is that this is all irrational, because the universe is only half dynamic. Since there's a requirement to make every bit of equipment in game playable, it makes it hard to have a genuine improvement because of game balance. I'm not sure what the in-universe reason is for the small armies, as far as I know there really isn't one, each State should have thousands of divisions they produce themselves, but I suppose that would eliminate the whole a Company is a powerful force approach.
I don't doubt the numbers are a bit wanting in terms of production while trying to tie in Star Wars like epic fights and battles the universe throws into the mix. From the earliest stories in the universe to the Dark Age we've seen a trend of power creep (both in Tech and in numbers) that did not keep in line with the idea of scarcity and difficulty maintaining stellar empires central to the BT Theme of high tech protagonists using their wit and grit to keep their machines going in the face of odds stacked against them. Abrupt insertions into the story-line of large numbers of 'Mechs popping out of the wood work is as common to the franchise as is maintaining a level of scarcity and rarity the universe continually demands. The Clans, Comstar Legions, "new Star League", WoB assault, etc., have large amounts of tech and activity come in seemingly out of nowhere leaving readers with a sense of struggle to come up ways to have it make sense.
Kind of like hammering in a square peg into a round hole.
So yes, I do agree when someone sits down and number crunches that things don't add up as nicely as it should. I'm sure every person that wanted to write a BT story would like to have at least done once in their stories a large epic battle.
That being said, if we remove the sudden glut of things constantly showing up in the universe we can understand somewhat more profoundly where the actual limitations in production would come about if things worked close to reality. The main limitation to churning out massive amounts of units are actually three things (so far that I came up with writing this): inter-stellar trade, communications, and lack of direct influence in local labor. Anyone wants to add more is welcome.
The majority of BT is risk averse and do not have an economy that works like we're used to here where you try to anticipate fluctuations in demand and respond to market forces. Interstellar communications is much too slow to respond in real time to a galactic market on the scale and size of BattleTech. So as is trying to calculate demand, which is why we're doing this number crunching in the first place, and leaves the various corporations risk averse to over produce and gain market control unless they have inside knowledge to do so OR have some form of guarantee they won't go under in the process.
If we remove communications as a stumbling block we then have another bottleneck of sourcing materials once we're going interstellar. This puts an upper limitation to the risk on what a corporation would produce and what raw materials they will ask for given that it takes roughly 1-2 months to ship things via freight in BT one-way. Also, it is prohibitively expensive if you wanted smaller quantity items (like a production run of small lasers or MGs) as it is normally easier to ship via freight a large bulk of raw materials or a large amounts of finished product to market. You will lose out if you're in the middle given the amount of fees that add up while trying to quickly sell something to an available market.
Now we come to labor and probably the most ignored part of the universe and yet the most relevant. When a corporation is ready to produce things, now it comes down to gaining enough skilled workers to produce as many things needed to reduce costs and increase profits. So, the majority of laborers are seasonal staff hired when things are ready for assembly. Additional pressure is also applied when you factor in the lack of direct influence said House Lord or Clan Khans has in the every day life of the folks at the near-bottom peg of society. These folks political allegiance is to his/her local assembly on the local planet and not his house lord, empire, or clan domain. There is no actual way to influence labor than through an equivalent exchange for services and thus limits the ready population of skilled laborers as full time staff to produce things quickly to market. The majority of labor ends up other labor intensive occupations such as mining or logging or in sustainable occupations like agriculture. Most of the universe was written before the large influence of automation we have today. Even if we tried to reason automation into the picture the costs of transitioning from a colony of settlers to a completely automated society costs way too much to organically achieve unless it is plot written. IF it is automated fully, then the laborer is completely liberated and I will leave it to the reader to make conclusions on how the universe would work (or not work).
So it's not really under production but rather only producing what is needed being
very close to Marxists type of economy where the worker is not bound as firmly to his/her means of production for survival and somewhat liberated from it. The poster boy of only producing what is needed is Clan Smoke Jaguar and probably the most true to marxists economy whether or not the authors writing the story arcs intended to be it.
I hope this helps as some food for thought until the pop corn is done from the microwave and another 10 legions of Space Ma... I mean 4 Regiments of 'Mech duke it out to advance the story line. >:D