I don’t have a problem with (or a say in) Georgia joining the EU but I worry that adopting the Euro will at some point harm smaller countries, especially those on the periphery. I don’t think Georgia is one but there are inherent trade-offs when you outsource your monetary policy to another country.
The U.S. dollar is used in a lot of places and the Federal Reserve does not take them into account at all. Often it’s used for stability reasons. But just as often, it can cause major hardship when there’s a recession or imbalance somewhere.
Politically, I think (or maybe assume) it’s good but from an economics standpoint, there’s a point when currency unions can be too large and it hurts the periphery. It might suck to have your currency weaken but it sucks more to adjust to the new reality the hard way (mass unemployment, usually). But hyperinflation sucks the most and more than 1 country should outsource their central bank and adopt a major currency.