Over the past 10 years, we have buried my mum and both my PIL, and we definitely did NOT have formal invitations, thank-you letters or favours provided by the funeral director, @Robin60.
We sent out letters ourselves - firstly notifying people that the person had died, and then notifying the date and venue of the funeral and wake, once those had been organised. We used mail merge, and printed them ourselves, and it wasn’t expensive.
I have never heard of favours at a funeral, though I do like @CharlotteSometimeslikesanafternoonnap’s relative’s idea of giving everyone a packet of seeds - I wish we had thought of that, as all three were keen gardeners, and would have approved.
The funeral directors did help us with the Order of Service - that was very useful, and well worth paying for, but favours, invitations etc does sound like an attempt to screw more money out of people at a difficult time - poor behaviour, imo.