Correction, you don't have to "greet" them.
I set up my Homepass last night, then went to bed. Woke up this morning to only 10 passes on each system. Googled what was going on. Misread someone else's description.
So, you get the notification "Hey, you got StreetPasses!" - When you click the gate icon, you're given three options (unless you've used your current StreetPasses in all the available games, in which case, you're just taken to the new StreetPasses).
"Keep Playing" - which is like cancelling out, allowing you to play whatever titles you haven't yet.
"Go to Plaza Gate" - Loads the next (up to) 10 Miis at your gate, just like before.
The third (new) option is "Send Visitors to line" - it pushes the new StreetPassed Miis to a line that you can then greet later, ten at a time.
So, you don't have to greet all the Miis, every time, but you *do* still have to fiddle with your 3DS every few mins in a crowded area. The funny thing is, I'm not sure why they couldn't just automatically queue new StreetPasses to the Visitor's Line and let you retrieve them, ten at a time, when you have time to play.
Basically, automate the "Send Visitors to line" option.