Was there motivational problems among Brits in WWI and WWII? Maybe there is difference when you train to defend your own country versus going to some foreign country to fight abstract and vague threat or advance foreign policy goals.

At least here in Finland the motivation comes from clear and well defined threat. Enemy comes always from the east, if we don't fight we suffer other ways.

>What do you do with a conscript who never wanted to be there and possibly fundamentally isn't suited to military life anyway gives up?

Conscription does not mean that everyone serves. Everyone is called to be evaluated, some are not called to serve, some are sent home because they can't make it.