That being said no individual state has veto power in the US. I don’t know anything about the EU but I suspect Germany and France or some other members will have to say at some point that this veto nonsense has to go. I doubt it can happen in our lifetimes as long as individual members are sovereign.
WRT to the "veto nonsense" you refer to: as far as I understand, the EU nowadays does have some sort of majority voting system for most areas, since the Treaty of Lisbon came into effect [1]. This also means that sovereignity of member states is already somewhat impaired (since any state alone cannot veto all EU decisions).
Veto is being slowly removed from most decision-making procedures. It's already not there for a lot of (most?) "simple" areas. In theory even the budget should be approved with qualified majority at some point in the next 10 years or so, if the European Council follows the roadmap that the previous Commission recommended.
I don't know your lifespan, but in the next 40 years I expect the veto to be limited to mostly symbolic areas, like defense.
