I'm personally surprised that blocks with lees number of transactions are getting higher fee rewards, but that's how it is.
Full blocks with fewer transactions mean wither a large number of inputs or output, since in this time no normal user is consolidating his wallet those mostly come from exchanges doing their payouts or moving their coins, and since for them time is essential and users already pay for these fees they afford to pay more. For example, one of my deposit waited for 12 hours before being confirmed at 10sat/b but in the next blocks the exchange consolidated some 30-40 deposits and moved them with a fee of 50sat/b, more than triple what it would have taken to confirm it anyway.
I got sent about $500 with 4 sats/byte, it took a whole week to clear, but it cleared! Low fee transactions are definitely still possible, just manage your expectations for clearing times 
For private stuff yeah, but you can't run a business like that.
Imagine a gambling site or exchange on which both deposits and withdrawals would take a week, nobody would use it.