It DID affect their fungibility, hence the reason people starting saving the silver coins and spending the others.
Spot price of silver in 1964 was $1.29/oz, and there's 0.18oz of silver in a quarter, so the melt value of the coin at the time ($0.23) was slightly less than the face value. I'm sure the government saw that silver was quickly going to be worth more than the coin itself, hence the reason they ditched the silver minting.
But the decrease in value didn't translate to market practices. i.e. it wasn't the case that a loaf of bread might cost $1.00 if paid by cupronickel coins but less (e.g. $0.90) if paid by silver coins which should have been the case if the two values had actually diverged.
Legal tender & melt laws. You can't legally melt down US coins and they must be accepted at face value (rather, they must not be accepted for less than face value, but you can pay more than FV if you really want). Since you can't legally melt and/or isolate the silver in a 1964 dime to create silver bars, there's no point factoring in melt value, maybe unless you believe the USG is on the brink of complete collapse where the laws become void. You must accept US dollars for any debts, which includes many (but not all) merchant purchases.
A $1-denominated silver coin deemed legal tender which contains $5 worth of silver is not worth $5 because the government demands it not be and will use force if you disagree. On the flip side, you cannot denominate coins with any USD face value unless you're authorized by the government, but there are ways to get around that, at least. For example, a Microsoft Point is currently the effective equivalent of $.0125. 5000 MS Points = $62.50 at current rates. Their particular transaction scheme lets them get around legal tender law and effectively have their own "inherently worthless" currency they mandate as being valuable (which they justify by offering goods and services for sale, payable with MS Points), similar to BTC except for the mandate. Theoretically, MS could devalue their currency if they wanted by simply offering less MS Points for more USD and making games/services cost more MS Points, which'd effectively be inflation. Actually, I think they deflate their currency, because from the quick Google search I did to find the market rate, it looks like it was $5/5000MSP a few years ago, so they're actually creating an incentive to buy and hoard MS Points even though you can never (by the EULA) cash them out for USD like you can with BTC or PMs.