As a note, the 7.7x58mm round was adopted because the 6.5mm round lacked stopping power. Unlike in an assault rifle, you can't just double tap an opponent. The first round has to make the stop.
I know that was the thinking, sure. I am sure the new round was more lethal, but I still think the 6.5x50mm was sufficiently powerful. Honestly, I think a lot of it was pyschological--the Chinese were using a bigger, longer-ranged round, and so the Japanese adopted one, too. Keep in mind that the long-range 7.7x58mm round was adopted for machine guns (where it would actually be useful, at least for interdiction purposes) in 1932, but they didn't bother making a rifle in that caliber until *1939*. To me, that shows that they didn't consider it a priority. The only real problem with the 6.5x50mm is that it doesn't yaw on entry, but that's common to rounds of the period.
One thing that I think points to the effectiveness of bullets in the 6.5 range: while during the 30's, Italy and Japan would move from this size to something bigger, after the war, *everyone* adopted something in this range or smaller. In my opinion, the 6.5x50mm was ahead of its time. While you are correct that part of this is because of the ease of follow-up hits, most of it is simply because 6.5 is the sweet spot between speed and bullet weight. If you are fighting within 300m, it'll put your man down. Most stories to the contrary are either bad luck or exaggerations. The 7.7 range will kill on the first hit almost every time, but if the 6.5 will do it 90% of the time, is it really worth the extra weight, fatigue, and reduced ammo capacity?