Like a church? A synagogue? A mosque? That fits the definition exactly. It seems like a substitute for a house of worship for people who do not believe in God.
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I might be very misinformed about how church works, but I think that coffee shops fill a very different niche. History kinda supports this: coffee shops became valuable places of business and occupied the 'third place' role even in extremely religious places and times (I'm thinking of Lloyd's specifically, and 17th and 18th century coffee shop culture as a locus for business ventures in the Netherlands and England).
Some do. Do people people go to sufficiently sociable cafés daily? Most people go with and talk to people they already know.
>and hold business meetings in church? Do religious people go to a church to do a casual date
Not in church, but with people they meet in church.
> or catch up with friends and associates
A lot of churches do have some socialising after services. Just serving coffee or something afterwards
Even without that people chat on the way out.
> on weekdays?
If you go to church on weekdays