Pretty sure TPCi is printing as much product as possible, demand has just never been higher since Pocket launched
From what I know with my own experiences (mass production printing), they do look to be at capacity with printing with very few solutions other than to expand operations.
Big post, I'm so sorry. "I ain't reading all that; congratulations, or sorry that happened." If I'm wrong somewhere and there's information publicly available about TPC/TPCi's processes that I didn't find, please correct me! I only know what I know from my experiences, and Pokemon Company is not among my experience (and I have other things to do than deep dive to find everything in one sitting).
Assuming that all sets in standard rotation are still being printed ALONGSIDE upcoming sets - maybe with the exception of some of the older sets expected to rotate soon, where they could be distributing warehouse stock instead - there's a certain amount of sets to be allocated to each machine. All these sets have different languages, some have special assets (like new unique artwork for promos, unique backs for the Worlds sets or foil/texture treatments), which further splits allocation of printing machines available for optimal printing.
Looking at Millennium Print Group alone, they have 18 UV print machines (Komori GL-40) in their currently operating pressroom. Each machine at maximum production can produce 2,081,200 cards an hour (the GL-40 has a maximum production of 17,200 sheets an hour, and PTCG is printed in 11x11 sheets; this figure is likely higher than what they're running at for QA purposes) and run 24/7. They print English/French/Italian/German/Spanish cards, so I'm imagining they have at least 2 machines per language on average with maybe a couple more for the more prevalent languages and shift things as demand... demands it.
The sticking point is that despite being acquired by Pokemon Company, MPG takes estimates and orders from other companies on their website. This means we don't know exactly how many machines are being used by Pokemon Company for PTCG at any given time at MPG, in exchange for profiting from a wide variety of businesses (apparently they print for "Education, Pharmaceutical, Retail and Entertainment industries" according to their Company page) seeking to print their work using MPG. This is pretty safe to assume the same for the Brazil and Belgium pressrooms, and puts a dent in how many cards get printed to meet demand.
If they're so dead set on keeping all their other clients (no doubt a big profit), they're going to have to either get more printing machines (big cost, as more machines may require bigger space, which means either moving costs or construction costs) or acquiring new companies (potentially bigger cost), all of which results in logistical and operational shifts. while pokemon company does make huge profits, japanese businesses are reaaaally risk averse, and what may be a simple solution to us requires a lot of corporate and bureaucratic steps to achieve. In the long run, it'd be great for daily operation, but the immediate costs and reallocation of resources (not just financial) are never fun to look at.
Ultimately, they don't stand to benefit by just continuing to print as normal- they see the demand, and they see the pressure on them to provide their clients (retailers) the products they need for operation. Expansion is necessary, and they HAVE made some steps (MPG has an EU pressroom, but it seems to not be ready yet since the website doesn't talk about it), but it hasn't been sufficient. I imagine when this EU pressroom gets up and going, they will take on more of the European language printing which would reduce logistics costs significantly (less international shipping from the US and US MPG pressroom could dedicate more machines to English sets), but heck if I know how long they're going to sit on this one unused pressroom.
