Why have this the day after a 3 day Yom Tov ??
Between Rosh Hashana and Shabbos if you wanted to you could connect with those people who you wanted to (Assuming they lived near you) and if they did not, you would have to call them after Shabbos to re-connect
People go to Shul on Rosh Hashanna and Shabbos, they go visit friends on Shabbos (Or go to the park) etc.