Good question. The problem with "rules", and kata, if I'm honest, is that we can forget what the real thing is like, and also the fear isn't there. I've done free sparing with bokken, (with someone I trust and who knows what their doing), and it's a very very different feeling than kata- you don't take silly chances, you try not to leave yourself open, and you're very conscious that it's dangerous. As one of my instructors once said; "There's a huge difference between Dojo techniques and what you'd do in a pub carpark on a Saturday night".
My uneducated opinion is that training only with a shinai, like training/sparring/competing only by a specific type of rules will make you good at using THIS tool in THIS context (e.g. one on one, same weight category, no kick to the nuts, etc.). But if it is another tool you add to your mix, it allows you to widen your ways of training and makes you overall better (given that you stay mindful of what couldn't be done in a real situation).
Something that some koryu do is at some point far enough in the training they have an instructor or a senior student with a less experienced student, and what they will do is they will "switch" kata mid "flow" randomly and without warning form one to another one that the lesser experienced student should know. This provides some spontaneity and need to adapt and react "on the fly" without becoming full on free sparring.
Im not personally sure that the shinia would have brought in competition fencing. Stick fighting was incredibly common throught history and across cultures, early modern england france america and poland, ancient egypt, the zulus, and tasmanians all have recorded full contact stick fighting sports that were utilized for sword/club training, several of those cultures would have done it shirtless. I imagine the pre shinai japanese would have done much the same. Just to note 19th century European militaries used both paired kata followed by free sparing to train soldiers in bayonet and sword practise for the battlefield. Funny coincidence mentioning the 19th century, Britain in the 1890s had the same issues of their training weapons not matching the real thing as Japan had in ww2. When the 1892 pattern infantry sword came out the army also adopted an Italian style gymnasium sabre that wasn't really close to the sharp one. Wilkingsons blade company was inundated with complaints saying they had been giving the wrong training sword as British practise had been up to that point to use an identical training sword compared to the real one.
My experience with martial arts makes me say that a little kata is okay for solo training, but working with a partner on drills, like pad work, and especially free sparring, is the way to go. For best results there needs to be an element of danger. Nothing too serious, sparring with bokkuto is too much because someone can be maimed or killed, but say with a padded sword you won't break bone but it will hurt. If there's no pain involved, even a little, or a punishment like doing pushups for each failure, it won't be as fun and won't be taken seriously. For a person to advance in skill, imo the best way is to find the right mix of fun and danger.