And, much like a beloved relative, our system has major annoyances and often keeps us waiting. (Can you still call Uncle Bob beloved after he shits the bed? I think you can.) But it's so core to the Canadian experience -- we all know, no matter what economic turns we might take, it's always there for us from birth to death, quirks and all. It's a constant and foundational.
I reckon by early adulthood many Canadians will have personally seen it help more loved ones than it harms (while asking for little or zero additional money) ... so I think the word beloved is reasonable.
I'd say our system is dear to my heart and that's synonymous with beloved.