The Jikishinkage ryu guys who practice occasional rules-bound semi-free sparring after a long period of kata training. In fact their kata training involves surprisingly limited contact for an extended period of time.
They didn't start to do this until they were no longer training for duels.
The Shumpukan apparently start beginners of Owari Kan ryu out doing shiai and then introduce them to kata later. If Josh Reyer still posted here he could share more on the topic, but I bet you a beer that's a recent institution as well. I'll ask my Sensei about it this weekend.
Anyway, you missed my point - I was responding to an anecdote that in BJJ, they have learned that getting beginners familiar with competition from the very start seems to get them up to speed in competition faster. My point was, that's training for non-lethal combat. if you are training for lethal combat, you had better not do a lot of freeform practice at the beginning, you'd be better off doing it like the guys in the first video you posted.