At my former Airbnb, since it was a separate and private part of my house, I greeted everyone. I pointed out things about the rental and the area and let them know I was there to help. In the 3 1/2 years I was there it was a win-win. After the introduction, some people I might not talk to again other than to greet, with others it was personal. This was a winter vacation hot spot and at the end I was pretty solidly booked for 6 months.
I would agree if I only had 1 listing but with 8 I would be running my self ragged just trying to get everyone let alone have any persona life. We have guests arriving everywhere between 3pm and 3 a.m. which is why I have self-check in which in my case has worked out very well for the past 3 years. Even though I don’t meet and greet unless they are just a 1 night stay I usually run into them at some point during their stay as I am there everyday and some times in the evening just to check in.
Because I’m only committing myself to two hours (between 4 & 6 as I said above) I can arrange my schedule around those two hours. It works well with our two listings and the one I look after for a neighbour. Many times this means that there’s an arrival every day but because guests can also self check-in, Ii don’t have clashes. Plus, I see it as part of the job. Mind you, I’m an obsessive scheduler 
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