Re: The problem with this is spending discipline
I'm not convinced the studies are going to be valid much longer. Sure, if you're used to banknotes there may be a disconnect but if you've been brought up on debit/credit cards then it likely means you learn differently. There is nothing stopping a youngster, with parental permission of course, from getting a debit or check card as many banks are now offering such accounts to children as young as 13 and it functions largely same as the adult version.
The fact that tangible bills aren't being passed about won't matter since the bills themselves have no inherent value other than that bestowed upon them by fiat. The only difficulty is going to know the exact "value" of the card since they can't simply open their wallet and count what is left. This is naturally where phones or other devices will come in being able to display the remaining balance. No, I think it's going to be more a matter of familiarity than anything else.
Consider that I don't carry cash and haven't for quite some time and I'm quite aware of how any purchase will impact me but of course, I was taught to throw nickels like manhole covers. The only reason I keep a few dollars in my pocket is for when I have to pay a toll on the roadway if I've got the wrong transponder since nearly none will take credit cards. In fact, I believe they are the very same bills that I put into the wallet when it was new quite some years ago and they are likely to be the ones which go into the next wallet as well.
I'll finish by saying I find the heading a bit misleading. The value of money is ambiguous since money can be the cash in your pocket or how much you have banked. The cash in your pocket is real tangible bills but that in the bank is merely a representation of value. To that end kids may never know cash nor its value but they will absolutely know the value of money in the bank.