Europe has far more to gain from NATO than the USA – even though of the EU states only Portugal is a necessary NATO member, the alliance’s essential function is to defend continental Europe from a potential Russian attack. The key members fulfill a strategic role that allow the USA to project military strength in the region and safeguard forward positions around Russia – all in favor of preserving the (usually western) European status quo.
In terms of direct US interests, this doesn’t really matter. It’s the US protecting direct EU interests, in an era where Russia is not capable of reclaiming lost Soviet-era provinces, let alone threatening western Europe, and the EU is increasingly unwilling to accept US influence. In terms of historic US military interests, Turkey is the more appealing partner than any EU member, even if the military interest is a Russian rivalry.
In fact, the EU has contrary interests in many cases. In terms of historic Turkish military interests, the USA is a more appealing partner than the EU, which actually opposes it in its interests. So why should the USA and Turkey break off their alliance over the EU, which they labor to support but conflicts with the two’s interests, especially when the two share those interests?
NATO relies on Turkey to protect EU interests. Turkey, like the USA but in a much reduced capacity, only benefits from EU/NATO members in terms of marginal influence which is increasingly rejected by Europe. The EU cutting out Turkey from NATO to let in more non-strategic members (though Finland would certainly be more useful than, say, Slovenia) would be an act of either utter stupidity or sheer insanity.
The EU needs Turkey in NATO. Turkey does not.