It's the only way to think of currencies. A currency is a tool for facilitating monetary behavior, and monetary behavior is about measuring delayed reciprocal altruism. Multiple currencies are as pointless and disruptive as multiple measurement standards (yard, meter, fathom, rod, cubit, etc).Its not fair to compare systems of measurement with currencies.
Out of curiosity, did you get passing grades in grade school math?As far as friction is concerned, "on-chain" exchanges like shapeshift could not be any frictionless. If Bitpay were to nativly support shapeshift.io, the only added friction is to select which currency you wish to pay with from a dropdown. Heck, a really well written wallet could automatically choose the currency to pay with based on the balances that wallet currently holds. Absolutely zero added friction.
In any case you've neglected the reality of spreads when it comes to currency exchange. Nobody works for free so there's always a positive cost associated with a conversion. No matter how low this spread can be made, it will always be a positive real number. All positive real numbers (review grade school arithmetic here if necessary) are greater than zero so no amount of shiny UI design will ever make currency conversion "frictionless".
As for the idea of holding a balance in every possible currency that you might want to pay someone in one day - if you think this is a good plan please diversify your savings accordingly. The advancement of the species benefits from the transmission vectors for retarded ideas losing as many financial resources as possible.