The Euro rifles are on the whole much better finished guns but also generally lower accuracy...
Not sure this is true at all. Any European manufacturer who won't gaurantee 1MOA out the box with factory ammo is going to really struggle and the American brands do no better than that. All European brands which I have personal experience with (Tikka, Sako, Sauer, Blaser), will do better than this with homeloads, but when you get to .5MOA or less, I reckon it comes down more to the skill of the handloader, the particular dimensions of that throat and chamber, the bedding on that specific rifle etc etc. Basically, all rifles I have seen on the market will shoot as well as or better than basically all shots, even off of a bench.
What I have found (in my admittedly limited experience) is that Americans want a 'value for money' rifle and are more willing to sacrifice fit, finish, trigger quality etc to achieve that. This is, IMO, a factor of the different usage and demographic in the respective nations. In America, the rifle is a tool, owned by everyone and used for a job. Not to say Americans don't love good wood etc, but the average american consumer is generally looking to spend much less on a gun and wants something serviceable, accurate and reliable, but not necessarily elegant. The European however, is approaching his rifle purchase from a long tradtion of snobbishness. He want a Rigby or as near as damn it in his Budget. Stalking etc in Europe has always had a slight whiff of gentrification, whilst American useage has not, and the equipment reflects this.
Just look at shotguns. The average American wants a pump or a semi-auto. It's practical, reliable, fit for purpose and easy to use. Also good for home defence. The Brit on the other hand wants a Purdey. Both want accuracy and fit. It's a cultural thing, and this extends to rifles as well.