England's line-up understandably carried an experimental air with so many first choices either unavailable or left on the bench, and it showed in a disorganised, uninspired first hour.
In the end, however, England made up for that poor start with a strong finish, even though it took the late goals from Alexander-Arnold and Kane to give their superiority an emphatic look.
Palmer's penalty, scored with his customary aplomb, will have delighted the 22-year-old forward who was surely on the plane to Germany even before this game.
His goal set the seal on a remarkable campaign that started at Manchester City before he left to become Chelsea's stand-out performer.
He has now scored in the Premier League, FA Cup, Carabao Cup, European Super Cup, Community Shield and now international football in a stellar campaign.
Alexander-Arnold's goal, struck crisply from Jack Grealish's cross, demonstrated what he can offer in attacking positions and made up for a poor first period, when he was surprisingly wasteful in possession. He showed his full range of passing after the break.
One of the big pluses was the display of Eze, who will be one of the players trying to force Southgate's hand, or prompt a late change of mind, before he trims his squad back to 26 following the Iceland game.
Other than that, there were few big takeaways for Southgate, few stand-out performances, leaving much still up for grabs in that Wembley friendly.
Southgate's selection for that game will reveal a much clearer picture of where his thoughts are heading as he targets another tilt at glory in Germany, where he and England will try to shed their 'nearly men' tag and end a barren sequence for the men's team stretching back to the 1966 World Cup.