I don't think the EUR is designed as a competitor or alternative "equivalent" to the USD. Rather, it is a "readily available" option --differing in a few substantial aspects (rather than outright mimic USD)-- for anyone, anywhere to consider at their own pace.

Even if "they" wanted to, they couldn't just, as in the past, once again "compel" the world to use their national currency for your reserves and trade-settling, then remove the backing, break promises and debase and inflate for 4 decades straight. No one would fall for it again, nor is it really desirable anyway for any productive (say, net-exporting) country.