I looked at mitzvos mentioned in Shema, and this is strange: nobody relies on OOT Rav putting tefilin instead of him, or a mezuza or wearing tzitzis, but somehow “shinantem levanecha” davka has to be outsourced to a local school at least, but better to a far away towm – until the kid is able to fly onhis own and go to another country.
More seriously, when Bava Basra goes through educational option: fathers teaching is preferred, but did not work consistently. Sending to Yerushalaim (i.e. best, most kodesh and inspiring places) also did not work for many. OOT yeshivas is 3rd option – but teens did not listen to the teachers. Last and accepted option was to teach small kids locally.
Furthermore, there were always differences in styles: In EY, kids would learn first (locally) and then marry (so not to be distracted). In Bavel, kids would marry first and then go OOT (not to be distracted) to learn.