NFL is an undisputed success, and if the ESL is anything alike, no club will even think about being owned by a state
By what metric is the NFL an undisputed success? Attendances? TV deals? Popularity? If so, by your rules the PL is a bigger success. NBC's renewed deal to show the PL in the US has cost them $2.7bn, but nobody is paying anywhere near that money outside of the US for the NFL rights.
Attendances are good, but so they should be when teams only play 8 or 9 home games a year. But ticket prices are eye watering compared to England, and as proven with the £77 fiasco, American owners with a majority stake in the game here would hike prices in a heartbeat.
And popularity. Well, biggest sport in the US for sure, but where else is it the biggest sport? How many countries outside Mexico, UK and Germany are clamouring for the international games? Compare that to the demand for English clubs to play everywhere and anywhere each summer in meaningless games.
The NFL schedule is also an indicator of popularity. It is geared to the domestic audience (nothing wrong with that btw) with kick off times for the biggest games completely incompatible for anyone in Europe or Asia to watch live. This is a clear sign that they don't believe anywhere near enough people are watching overseas to make kick off times a little easier for them.
You also asked how many NFL teams had moved cities in recent years? Well, define recent I suppose. Last decade or so is recent for me, so 3 teams, and one has moved an hour outside of its home city as well. Two of those teams struggle to have even half of their stadium cheering for them in home games most weeks because the support for them is negligible given they played elsewhere for decades beforehand. Not something I'd wish to see replicated even once here.
So yes, the NFL is a success, in its own country and as a niche alternative in a few others. But it's miles behind European football in all the key global metrics that anyone would use to denote success or popularity.