I wouldn’t (and I’m American originally).
Guns - shootings in shops, festivals, markets, churches, schools and more schools. Your children would grow up in fear if being shot and have to practice active shooter drills in school.
Medical care will cost so a few grand a month for insurance - that’s without paying the deductible. That “savings” you made is easily widdled down if anyone gets sick/injured.
Schooling is not on par. Will you be paying for private school (there goes that extra money)
Flights home to see relatives - does company pay that? If not, there goes more of that extra money.
Look at the exchange rate. Pound isn’t so good due to brexit so right now looks attractive. But when the pound recovers, the $5k will not be (let alone all the extra expenses)
You do gain likely living in a much larger house, air con, big fridge/freezer. Built in swimming pool, two BIG cars, cheap petrol, cheaper food (but much more full of all sorts of nasty, full of corn syrup plus things banned in the EU - just read up on Kraft MAC n Cheese, USA recipe vs EU).
Be forewarned, if you get a green card, you’re required to pay tax on your worldwide income/investments and report to the IRS all your bank accounts anywhere in the world (look up FATCA and FBAR).
Lastly, there’s also the matter of Trump.