Motor Trend has attempted to make a magazine somewhat in that mold, called Motor Trend Classic. It is very good--or at least good by American standards. But it's also quite expensive (knocking on $15 per issue) and sales are therefore very low. It's not profitable even at that price, and is mostly a vanity project for the editor; profits from the rest of the vast company empire support the losses that MTC supposedly endures.
We also used to have Sports Car International, which was a very nice little magazine, run on a shoestring budget by a very, very old-school company. They refused to adapt modern techniques to solicit advertising, despite my friend's attempts to drag them into the 20th century. That was a magazine that was also losing money but was supported by the other magazines in the family (Ross Publishing, they do Corvette, Porsche and Ferrari magazines). Eventually SCI slipped under the waves as well.
Fortunately the British magazines enjoy wide circulation in the USA. I subscribe to Classic & Sports Car, which I think is the best of the lot.