SMGs? Hell, they stuck that shit on their fucking LMGs:
View attachment 1744098
In all fairness, however, the Americans were really the only ones to achieve ubiquity with semi-automatic weapons. The Soviets messed around with them (SVT/AVT-40), as did the Germans (Gweher 43), but it wasn't really until the SKS and the FN FAL that semi-auto infantry rifles became the norm, and were swiftly replaced by assault rifles.
There is, however, the question of doctrinal thinking. The Russians were trying to arm a million men as quickly and cheaply as possible, so expensive cutting-edge tech was in many cases out of the question, while Germany didn't have the industrial base to properly equip its armies at the start of the war, much less once the strategic bombing campaign started. Only America had the trifecta of industrial capacity, R&D budget and "bullets are cheaper than lives" philosophy to make the Garand work. So, then, what was the roadblock for the Japanese? Probably the industrial one, given how many crazy prototypes of all sorts of things they got around to making, possibly combined with an unhealthy dose of bayonet romanticism, US Marines-tier marksmanship obsession and/or an over-reliance on the machine gun as the volume of fire producer for the squad. If there was any army that really needed semi-auto rifles, it was the Japanese, what with their usage of magazine-fed machine guns meaning that the weapon is going to have a lot of downtime, so I suppose I should do some looking into why they didn't pursue that avenue.
EDIT: regarding that addendum of yours, that would make the AR platform a battle rifle, but the term usually indicates the use of a "traditional" rifle-caliber cartridge, such as .30-06 or 7.62x51 NATO. Semi-auto intermediate caliber rifles sit in a weird spot of not really having a unique name unto themselves, likely due to the aforementioned introduction of the intermediate cartridge alongside the assault rifle, and most semi-auto intermediate caliber rifles in production these days are simply civilianized versions of assault rifles that have had one of the essential qualifiers for being an assault rifle ripped out.
EDIT 2: Ah, shit, we got our asses yoinked across threads.