The danger of no Primary Key when replicating in RBR (and a partial protection with MariaDB 10.1)

TL;DR: unless you know what you are doing, you should always have a primary key on your tables when replicating in RBR (and maybe even all the time).

TL;DR2: MariaDB 10.1 has an interesting way to protect against missing a primary key (innodb_force_primary_key) but it could be improved.

A few weeks ago, I was called off hours because replication delay on all the slaves from a replication chain was high and growing.  It was not the first time this happened on that chain, so I thought right away that this was probably an UPDATE or DELETE of many rows on a table without a primary key.  Let's see what is the problem with this and to understand that, we have to talk about binary log formats.