All true, but I think it's worth pointing out that the "seriousness" you're talking about was a luxury that few could afford. Those who pursued budo, or koryu before them, were not what you could reasonably term productive members of society: they and the arts they practiced were luxury items, each of which required a certain number of productive members (rice farmers, fishermen, craftsmen) to support him. In economic terms, the budoka you describe is a member of the leisure class, and in societies that lacked the resources, knowledge and level of social organization to create the surpluses necessary to support these luxuries, a leisure class simply didn't exist.
The old bushi were not of a "leisure class" because they didn't train primarily for interest or self-satisfaction: it was their duty, and when duty called, it was their life on the line.
Moreover, the ability of society to obtain the resources, knowledge and level of social organization to create surpluses depended on someone to prevent others from stealing those things. You had to have warriors with skill to fend off brigands and gangs of thieves, a la The Seven Samurai. Of course, The Seven Samurai was a rather late-Samurai-era story. In the beginning, the fighters were farmers and fishermen gathering to protect their homes and villages. But as the thieves and brigands (the true leisure class) grew stronger and more skilled, civilized people found it necessary to form a warrior class, whose sole job was to become strong and skilled to allow the farming and fishing specialists to work and live in peace.
Moreover, while the farmers and fishers could relax and have fun at the end of the day, warriors were bound to step carefully everywhere they went and at all times, lest some casual remark spark the anger of a stronger man, or some close friend stab you in the back because he was paid off by an enemy.
Still, the bushi had their own families and beloved people and their first motivation was to protect them and their society above themselves or their own pleasure and interests. And their waking hours involved hard training and self-sacrifice. It was far from leisure pursuit. And they were far from non-productive since all organization would have been destroyed by thieves without them.