It wouldn't have been possible for non-spellcasters to both avoid combat and advance; Bushido split experience into Shugo (which applied to Shugenja (mages) and Gakusho (priests)) and Budo (which applied to everyone else). Budo was acquired almost exclusively through kills (which went to whoever struck the killing blow, to the point I still hear some people who played in those campaigns joke about someone "stealing the budo" when they'd been ineffective in a combat until they managed to get in the kill.
My guess would be that they only rarely ran into samurai with the necessary skills to pull off those sort of effects, and probably later in the day; there were a wide variety of opponents who were far from that dangerous (including most of the two varieties of mooks).
In other words, it was either overuse, or (if using the random encounter generation tables) bad luck of the die throwing up one of the most deadly opponents. Not a problem in those days that could be limited to Bushido.
I don't honestly recall much about playing casters. Aside from 'Kung Fu', the David Carradine TV show, where the the main character doesn't particularly evince any sort of mystical powers and beats everyone up, there really was nothing but Samurai and Ninja, and maybe a smattering of Yakuza as tropes that anyone in the US understood. Nobody could even tell you what a 'shukenja' or 'gakusho' was, let alone wanted to play it! Not saying they don't look like interesting character types to my eye today, but in 1978 we were 16, shallow, and wanted to kill things with curved swords, basically.
I suspect the people you are referring to simply played a bunch differently from that. My experience with Samurai in that game is that, unless you really built a sub-optimal character, you were kind of a combat monster after a few levels and out of everyone else's league in that department. So, NPCs, same way, if the GM unleashed such on you, you better run. Yes, there were 'mooks' and killing them was a cheap way to get XP, but also generated a lot of enemies, as the setting is after all one of a highly cultured, but violent, society where making enemies is both a bad idea, and inevitable.
Anyway, all I can say is, the campaign I played in was very interesting, to me at that time, but also super lethal. Surviving to even get one level of 'budo' was hard, and only a few players managed to ever hit level 3. I left after a couple years, but I think the GM eventually ran out of players and went back to running D&D or something.
If I was going to run a game of that ilk today, I'd consider starting with FitD and building a game based on clan/family competition and infighting. It could probably heavily mirror the factions architecture of games like BitD, but with different flavor and such. I'm not sure how much magic really belongs in such a game, at least at the PC level. Various types of spirits and such certainly factor a lot in stories, but they are generally defeated without resorting to 'magic' per se. A Shinto priest might be a sort of NPC you bring in to deal with specific problems, or perform necessary rituals, etc. and maybe to act as a patron. Certainly in later Medieval Japan the Buddhist institutions are more political than religious and might simply be considered factions unto themselves. As they tended to be egalitarian their fighters were a bit differently trained and equipped than the bushi, but not that much different.
Anyway, I wouldn't use Bushido, it is overly complex, probably not all that accurate a depiction to start with culturally, and just plain clunky and posessing all the characteristics of traditional GM-centered games of its time period. Reading over it now, I can see that the author was deeply engaged with the subject matter, but the game design feels amateurish and frankly obsolete. It would probably be best if some Japanese people actually wrote this type of game instead of some Americans who can at best claim 2nd hand knowledge of the material anyway.