I'm wondering about the automation as well -- this is something I would use, between buying/finding stamps, envelopes, etc...I rather pay a premium for the few times I need to snail mail something.
Envelope inserters of any decent quality start at about $40k and work their way up. And those small ones will do DLX only.
The biggest issue with inserters though is volume. Unless you are running them pretty much every day, they tend to break down. It sounds a bit counter-intuitive, but a lot of the rollers, etc all push down on each other and unless they are moved regularly, the develop square spots and then have difficulty picking up/moving paper.
As far as I'm aware, there is no integrated printer/inserter available. The best you can find is printers with inline z-folders (fold A4 in 3 to DL).
You wouldn't really want an inline solution anyway because a commercial folder/inserter can process much faster than most sub-$1m printers can print.