But for Jude Bellingham's 96th-minute equaliser against Slovakia, Southgate would have been out on 99, almost certain to have stepped down, and with all his previous good work quickly forgotten in the fallout of an absolutely wretched performance by his players and an inexplicable one by him.
Because England went on to win that game, however, he could yet join Alf Ramsey as the only England manager to win a major trophy having already matched the 1966 World Cup winner as the only other one to reach a final.
Any analysis of Southgate's tenure needs to be seen in the context of where England were when he took over.
In the 2014 World Cup, they finished bottom of their group with one point - their worst-ever showing - and reached their modern nadir with the humiliating defeat by Iceland in the second round of Euro 2016 that left a huge gulf between players and fans as hapless boss Roy Hodgson departed.
When Southgate took over in 2016, England were ranked 12th in the world and in total disarray.
Eight years on, they are the only European team to have reached the quarter-finals of the last four major tournaments.
They appeared in a European Championship final for the first time, losing on penalties to Italy, reached a World Cup semi-final for the first time since 1990 and lost out to France in a classic 2022 World Cup quarter-final that could have gone either way.
They have lost once in 35 World Cup and European Championship qualifiers and, against Colombia in the 2018 World Cup, ended a run of five successive penalty shootout defeats.
Ahead of the Switzerland game, they have won seven and drawn four - if the Wembley shootout defeat can be called a draw - of their last 11 European Championship finals matches.
Mentality Change
Alongside those impressive statistics, or perhaps the driving force behind them, is the sea change in mentality and culture that Southgate brought to England.
From day one he recognised his most important task was to stop players dreading leaving their clubs to go on international duty and he gradually helped them to love it.
Instead of fearing, even hating the English media, Southgate, embraced it. Unfailingly honest, thoughtful and considerate, he knew that any success had to be a partnership between all "stakeholders".
As part of that, he worked tirelessly to build strong connections between the international age group teams and left no stone unturned in terms of seeking outside help and influence.
As the man who missed the penalty that lost the Euro 96 semi-final shootout to Germany, he was better placed than anyone to know England's relationship with penalties needed fixing and threw his support behind a remarkable 18-month project that paid off in the win over Colombia.
And yet, Southgate could, and many argue should, be already getting ready for his knighthood, with England's trophy cabinet now containing more than just a dusty replica of the Jules Rimet Trophy.
His critics suggest he has managed to blow repeated glorious opportunities, not least by failing to make use of a series of kind draws.
At the 2018 World Cup, an easy group stage set them up for knockout games against Colombia, Sweden and Croatia while at Euro 2020, although they had an impressive last-16 win over Germany, their other opponents en route to the final were Croatia, Scotland, Czech Republic, Ukraine and, in the semis, a Denmark team who had lost their first two group games.
The 2020 World Cup pitched them against the United States, Iran, Wales and Senegal before the France defeat, while in Germany they have avoided all the big guns, stumbling past Serbia, Denmark, Slovenia and Slovakia. If they beat the Swiss, they will face either the Netherlands or Turkey in the semi-final.
Amid all those opportunities, perhaps Southgate's biggest failing is that, when glory was within touching distance, he seemed to freeze in the headlights.
The Croatia semi-final and Italy final were almost carbon copies, as England were on top, went ahead but found themselves being overwhelmed as their opponents' managers made changes that influenced the flow of the match and Southgate did not, or left them too late.
That "paralysed" approach was at its most astounding against Slovakia when, despite not managing a shot on target for more than 90 minutes, he waited until the final minute of stoppage time to introduce substitute striker Ivan Toney while the entire footballing world was screaming for change.
Southgate got away with it in Gelsenkirchen, just, and still has the chance to go all the way. However, the more likely outcome is handshakes and hugs all round as he heads home to watch the final on TV with his head rightly held high, but just missing the crown.