Well, the US did develop selective-fire weapons over time, but after WW2 the focus was on demobilisation and rebuilding, not issuing new rifles. The main opponents of the US in Europe, the Soviet Union and its allies, were still using the Mosin-Nagant, and upgrading to the semi-automatic, full-powered SKS carbine, so there wasn't any need for an untested design in order to establish fire superiority. Then atom bombs, mutually assured destruction, and it wasn't until the Vietnam war that the infantry of the US Army faced strong enough opposition that their M14s (effectively upgraded Garands) were shown to be outdated.

As for why the US didn't adopt the STG44 specifically, it had a few issues that other people have mentioned. Plus, it wasn't American - it would be a fairly humiliating thing for the US military, the most powerful in the world, to take a look at their defeated enemy and say 'actually, his gun is so good we want to replace all our weapons with it'. Plus, adopting a new weapon is more or less certain to come with a whole host of teething troubles, from design problems to supply chain issues to opposition from generals to complaints from soldiers; it just wasn't worth it to the people at the top.