FWIW we were trained to do shihonage the same way as well. No big breakfalls there. Kobayashi-sensei apparently felt that it was more dangerous than it had to be given alternatives and that an attacker not trained in ukemi wouldn't take that fall anyway. And from what I understand (and have seen in videos) when Tohei was demonstrating especially in more jiyu waza-like settings you'd see his kotegaeshi and shihonage done without the big fall. Things got much smaller, compact and efficient. Which is the direction we went all those years ago.
And for those lurking I'm in no way saying I feel any particular way is superior. It's just how I have been trained. It seems to me that any number of approaches make sense given their larger contexts. Give and take, pros and cons... They all balance out in their own way (ideally).