To answer your second post, yes, lots of us travel to the US from Europe for holidays.
In my case, many years ago I worked in LA, travelled around California a lot then, went to Vegas etc. Since then have travelled solo and with friends from the UK to various bits of the US. Used to go to US annually for a skiing trip with a friend.
Not with tour groups though until recently when, in the recent past, I did a 17 day US tour with a UK travel group starting in Denver. A bus trip with stops Cheyenne, Laramie, Mt Rushmore, Badlands, Deadwood, Little Big Horn, Yellowstone (2days here), Grand Teton, Arches NP, Salt Lake City, Arches, Mesa Verde, Monument Valley, Grand Canyon, Bryce, Zion and finishing in Las Vegas. It was great.
I travel solo, so in recent years have travelled with various UK tour groups to Asia, Central America, Africa, the Middle East etc. ie places where it is more difficult to travel solo. In Europe its pretty easy to book a flight and an hotel and just head off for a few days, so wouldn't really think of a tour group.
There are various tour companies in the UK that do these sort of trips. They are all a bit different, might have slightly different clientele from each other (by age or affluence etc). The size of the groups can vary hugely - my US trip, for instance, had 17 on it but sometimes it can be as high as 35 - so I was lucky. I have only used a tour group for a Europe trip once - going to Sicily - a terrific trip. This one I went with an outfit called Voyage Jules Verne www.vjv.com.
I was actually due to do another US tour next month - starting Atlanta and doing a loop taking in Nashville, Memphis, New Orleans and various other stops.
If you want to have a look at UK holiday companies that do tours, websites for solo traveller holidays would be www.justyou.co.uk www.onetraveller.co.uk. For couples (and solos) www.travelsphere.co.uk www.titantravel.co.uk www.vjv.com. There are many others.