Good points, I hear your concerns.
Thing is though, given most people's relatively meagre imaginations with passwords, I'd imagine compromising one
password / PIN from the average member of the public would open up access to all sorts of services, especially internet
ones. Most people have pretty lame, easy to guess passwords and tend to secure everything with the same one - the reason they choose one is precisely the reason that people would ultimately prefer one card to do it all - convenience. But, it's a truism that whatever is easiest and most convenient, often has many pitfalls. The story you tell is exactly the sort of thing that would make such a card unacceptable. Thing is, that story was nothing to do with the card, just the ineptitude of the bank. Let's face it, banks only put in ATMs to save them money, they never go out of their way to make it easier for you to get at your cash for your convenience.

I think it all depends on the security of the information on the card and the method of granting access.
i.e. PIN numbers for cards are generally 4 digits but people find it relatively easy to remember landline telephone numbers, so 7 digits should be ok. Given that and say, a 3 attempts and you're card is locked + 24x7 helpline number to sort out any problems like the one above, should make it relatively secure. Granted that'd be hard for older folk which would be a big problem. I think a PIN + some sort of biometric would be required - fingerprint, retina etc. That is a way off right enough, so maybe we will be arguing about the pros and cons for 10 years+ before this is remotely practical.

I think if government doesn't do this, some enterprising company will do it anyway as the increasing number of passwords etc will make it more attractive to people to get one access method for all these services.
Difficult to imagine who would be trusted to run it though.