Players who belong to a franchise that is moved to a new city will have to "up sticks and move their lives and families" whether they like it or not. It matters not whether that new city is Los Angeles, Toronto or London. There will still be upheaval.
Of course London would be further (but not much further than New York to Seattle, say). The culture would also be unfamiliar. And sure, that might put off many players. But I am quite certain that there are other players who would relish the experience. London is one of the greatest, most historic, most fascinating and most exciting cities in the world, after all. So it might well look, to the adventurous player, like an attractive proposition by comparison to Detroit, say.
Besides, the NFL regular season is only four months long. Pre season could be held in the U.S. It's not like the players would have to spend the entire year in London if they preferred not to. Even during the season itself, the London franchise would likely, as a general rule, play two games "on the road" consecutively in order to minimise transatlantic travel. So, in fact, the players need only spend some two months of the regular season in London. That's really not such a hardship nor a deal breaker.
