Earlier quoted context omitted.
The EU has a lot of carrot for countries like Poland or Lithuania. Even longer term members such as Belgium, etc, that don't have such history with the Soviets know they are better off being in the EU than splintered.
What is the 'carrot' for Spain, France, Italy that goes beyond what the EEC provided? Why would a 'really great trade agreement' not provide 'most, if not all of the carrot' with respect to economic upsides? Does the EU political apparatus an ECJ, i.e. beyond comprehensive trade agreements, provide carrots?
Less reductively, I think that a major benefit of a political union is that it gives some degree of democratic legitimacy to decisions made about difficult region-wide issues like trade policy, consumer protection, immigration, the environment, and anti-trust law, to name but a few.
All of those matters could in theory be settled via multi-lateral treaties, but they would probably be hard to reach flexible compromises over while still being overseen by representatives voted for by the public with a mandate for deciding on those supranational issues.
[0] https://en.wikipedia.org/wiki/European_debt_crisis#Spain