It has to be noted that whether or not a country's units or government would continue fighting even after their largest cities have been taken is mostly speculation, as we only have a handful of examples in WWI, namely Belgium, Luxembourg, Montenegro, Serbia, and Russia. Of these, only Belgium, Serbia, and Montenegro had a choice, as Russia collapsed from within as well and Luxembourg, barely having an army, was overrun.
Meanwhile, alternate history scenarios such as, say, whether the Bulgarian army would withdraw to Eastern Thrace or large portions of the French fleet would defect to the Royal Navy after surrender are impossible to figure out. With such a small sample size, the in-game premise that if you lose this, this, and this city you capitulate is fishy at best.
Maybe in future versions of Strategic Command we could have a morale indicator for each minor as well as each major so that we can avoid these issues, with each country only withdrawing if their morale hits 0. Instead of simply keeping you in the war, capitals should be focus points for recruitment and reinforcement. If World War II is any indicator, it is that, unlike France, most countries will choose to fight in exile if they could.
Yes I think you hit the core of that problem: Since the little ones have no NM on their own, the only mechanic available for determining when they've had enough is the capitals. But introducing NM for minors is probably a very major change, if it's even possible.