If we standardize our army's structure (i.e., the 1st Guards starts being a proper regiment instead of an over-hyped battalion, we standardize on 3 companies per battalion, and the 3rd gets a third regiment) and give each squad a LMG, we're looking around 300 LMGs with our current army. If we expand to two brigades, it's 600. An army that could oppose the British or Italians would need thousands. That's gonna be expensive, and suggests that license production will be more cost-effective than purchasing them. In a period where foreign exports of steel are slowing down, domestic production in steel-adjacent industry is also an opportunity to make sure workers in Reewiin stay employed.
We also want to get machine guns into the hands of soldiers ASAP. It's an important part of modern tactics (for the reasons Artificial Girl pointed out), and will the foreign ideas really help with the initial rifle training? That'll mostly consist of "here's how to shoot a rifle properly, here's a hundred rounds of 6.5x50 spitzer, shoot that piece of paper we stapled to a post". We've gotta get the basics down first.
Machine gun procurement isn't competing with things like training either. We have a slot that has to go towards weapons procurement no matter what, so unless there's something we want to buy or start production of that you think takes priorities over MGs, it seems fairly inevitable we'll use it for that.
As for autocannons, I'm not prioritizing it yet, but we'll need a 37-40 mm AT gun by the end of the decade (a quick review of the progression of armour on proper "tanks", even in 1931, and looking at Reewiin's geography and thus engagement ranges, the 13.2 clearly won't cut it for long). If we delay the Analysis option by a year, we'll hopefully learn that the Italians and Swedes both are working on a medium AA autocannon that'll also be useful for AT work, and then in 3-5 years, once we finally have the money and the support structure for a heavier replacement for the 13.2, we know replacements exist and we can buy them from the Swedes/steal them from the Italians.
