Why a multinational carrier remains difficult

Could NATO members pool resources for a shared carrier battle group?

Only with genuinely institutional ownership. A carrier is too central a national asset for one country to own while others merely contribute.

Sharing an expensive CATOBAR carrier and its group is attractive in theory, but a carrier is an unusually national political and military asset. A member government would face difficult questions over deployment, command, risk, and refusal during a crisis. Shared ownership would require an institution such as NATO or the European Union to buy and control the ship directly. Political sovereignty is as serious an obstacle as shipbuilding cost.