Combining EU's GDP like that is misleading. Lets not forget that EU is a very loose group of different countries. And the distribution of wealth is very uneven.Combining poorer European countries GDP with the likes of Germany gives the impression that "they are not poor" whereas they actually are. So spending 3-4% on defence might be bearable for some countries, its outright economic suicide for the others.
You are right about their military doctrine though, and i think its the smart choice. Reminds me of an annoyed American Defence secretary who complained about NATO's military capabilities just before retiring a few days later.
The problem with EU was, they try to create a battlegroup type brigade while putting the defence under the unified command. Which would mean the EU, not the respective country to finance the operation. Hence if we are to discuss the current defence situation of EU, we need to think EU as a whole, instead of just 28 countries.
Indeed if you are trying to compare the GDP of Greece or Spain to the big 3 (Britain/French/Germany) it would not be comparable, however, with a tiny amount of input of Greece, you would be supplemented with a larger contribution of like Italy or France for their respective battlegroup. In the end, it would be the same,, it would have been the bigger country drag on the smaller country.
EU as a whole would not gather a large force, like the American or even China, but the problem with EU is they are not poor in general, yet they refused to spend on defence is something people up there should rethink about. They think as an unified command, but they do it individually, that's why I said nobody are going to take the first step unless EU itself started to take the defence situation seriously, either group it together, or let them have their own, otherwise it would be like the current situation now, which is going nowhere.
While i generally agree with what you've said, i also think that if you in some theory (more like fantasy) put all the major assets of EU militaries together and orientate them towards a single objective, that would be quite a formidable force. Once you start adding the numbers up it doesn't look that weak at all.
Although under a condition, if it is in reality like it is on paper, not like for example the recent articles from Germany that were speculating only 4 Typhoons were operational iirc.
What you are saying is what they should do, however, the reality is not quite the same.
For example, if Russia were to invade EU tomorrow, the EU Battle-group would and could only fed into the fight piecemeal, problem with geological location, readiness time and mobilisation time are varied from different battlegroup. You would be most likely to feed Nordic and Balken Battlegroup into battle first, that's some 4,000 soldiers, then wait for the larger battlegroup to mobilise, it would take 4 days to a week for larger battlegroup (Such as French/Germany Battlegroup) to deploy, meanwhile the closer battlegroup and local defence force would be the only one that stopping the enemy invasion.
If EU were to deploy their troop with their Unified Command, they should also position their troop accordingly, which would mean a heavier present to the East and less dense position to the west. Where other problem such as training and integration as well as logistic now still fall on local member to take care of, yes, if you put all EU forces together , it would be a force to reckon with, however, currently it's not the case....
Don't know if you understand what I meant....