The only common goals that brought us together as far as the UK voter was concerned in 1973 was what was called "a Common Market", later to become the single market. In order to access that market with what was then 7 Country's and then 9 later to become 28, it seems by stealth and contract, regulations were introduced imposing the four freedoms into effectively business contract on trade.
Later of course the EU introduced greater controls through it's own Legal system, single currency, created citizens for it's non existent Nation, by issuing all it's member Country's citizens with and EU Passport, making us Citizens of nowhere, since the EU is not a Country these along with other 'State like" Governances, gradually absorbing the freedom's, laws and sovereign nature of Nation members. The further into membership the more the Nation state of that Country diminished. The EU is not a Country, it is not a Nation it is a trading organisation with machinations to be a super state.
Country's are held into what you call 'common goals' by trading agreements. Country's have no choice, it is blackmail, once the agreement expires you either sign up to the EU rules and regs of which there a thousands as well as the four freedoms or you have no access to the single market. Switzerland although only and EFTA Country is tied into the EU because it has foolishly become dependent to the tune of 66% of it's trade is in the single market. The Citizens want to end free movement, they can't because their bilateral agreements will not be renewed without signing up to the rest. Eggs in one basket.
You talk about more extreme members, you will have to be a lot more specific otherwise I can only guess at who you mean and what the extremes are.
As for the 'present leadership' I take it that you mean the EU leadership, since they are unelected the change can be instant if someone is dismissed, or moves on. If after attempting to renegotiate for eight years Cameron and his team got only minor adjustments on very important issues to the UK, it is highly unlikely that the EU will ever move on it's four freedoms, multiple rules and regulations, hugh membership fees. The very reason that the UK is leaving the EU is because of the intransigence of the EU. So Cameron did try, and promised that we would have a referendum in 2015 if he failed in his last series of negotiations, essentially he did fail and we are leaving.