You're judging Southgate against the high standards and expectations he has created which is unfair IMHO.
As
@BoroMart said you can't judge a manager solely on whether he has won anything. If during the shambles of England v Iceland someone had offered you the next manager (ignoring Allardyce!!) would take us to a WC Semi and a Euro Final you would have snapped his hands off. There are fine margins that have defined Southgates tenure and had they gone his way he would be lauded as one of the greatest international managers. Kane squares for Sterling in the Croatia game, we go in 2-0 up at half time and IMO we win that game easily. In the final against Italy, Rashfords penalty is so close to going in. He scores that, again I'm sure we go on to win. I know this is if's and but's but these fine margins are why you can't simply judge a manager on what they win.
Has he improved the team? Yes, undoubtedly
Has he given us some great times and memories? Again, yes undoubtedly
Is the squad in a good position going forwards? Yes
Also people seem to ignore the impact Southgate has had in developing the FA DNA and developing squads and players from the youth teams upwards. Someone made the comment above that Southgate inherited a good squad. Yes he did but that wasn't by accident or good luck. He was heavily involved in developing those players through his various roles at the FA