Yes, it makes sense to use metal-backed currency in today's world, because metal backed currency is not only more stable, but it also protects the currency against inflation. Of course, governments don't like this, because then they can't inflate the currency in order to raise money for government projects. But for the actual people living and dying with the currency, it is much better.
Yes, it makes sense to use a metal-backed currency in today's world, because metal currency is stronger and less liable to the problems caused by inflation. If the currency is backed with gold, investors and those buying and selling in the economy have more faith in the currency. Citizens will not lose their life savings because of inflation or a panic.
Backing currency by metal is at least a better plan than backing it by nothing, which is what we are currently doing. Right now we can print money with no real resource behind it to make it have real value. Having our currency backed by something, including metal, would at least have it worth something.
While paper money in the United States used to literally be a promise that was backed by metal (redeemable in gold or silver), this is no longer the case, and we have more paper money than we have what it used to represent. Our entire economy would have to be changed in order to have metal-backed currency. We have become too reliant on the current system to ever go back to the old one.
Using metals, especially precious metals, to back currency in contemporary society is pure folly. The prices of gold, silver, platinum and iridium change daily and can go up or down. Gold has lost a quarter of its value over the past year. Why are precious metals labeled as "precious" anyway? Just because gold, silver, platinum and iridium are shiny doesn't make them valuable. Gold is a great conductor of electricity, but its ornamental value has been a human fallacy for millennia.