The English coach has suffered from too much criticism and attacks by sports pundits and ex-footballers. Nobody expected the three loins to make it to the finals. But we saw how the team improved as the competition progressed. Gareth Southgate will remain the most successful English coach after taking them to two successive finals. He doesn't deserve to be sacked because many coaches have not even been able to make it to the quarter-finals of the competition. I think the English FA will not sack him, he would be allowed to keep improving the team.
Regarding the late introduction of Cole Palmer, I think it was a tactical strategy. Each time the Chelsea player is introduced with Ollie Watkins they end up getting a goal. You don't expect Southgate to keep Harry Kane on the bench, he is a player who has a lot of experience and should be respected. You will be surprised that Palmer would have been inactive if he had been played from the beginning. Kane will soon retire from international football and Cole Palmer's time will come. England has hired bigger coaches but none of them have achieved what Southgate has done with the team.