He was #2 in a system where #2 didn't actually count for much because the whole of society was so distorted around All Might. That was his whole deal, the symbol of peace, a hero so strong he couldn't be challenged by any villain, and so by his mere existence he discouraged them from acting.

And Endeavor's whole obsession with raising his successor was also distorted around that, because all he cared about was raising someone to one day outshine All Might or his successor.

Endeavor's position is not as solid as you think, partly because the society in which he holds that position is going to undergo serious upheaval and partly because he has serious personal and constitutional deficiencies which are going to cause him difficulty under the increased scrutiny he is going to experience, especially now that one of the major media networks is actively hostile to the heroes.

The next arc is going to be bad for Endeavor, because that's the natural progression of a plot where hero society is under existential threat from rising villains.

And this is not going to come as a surprise to people who understand where his character is.
It seems that your missing how being the #2 in a system where the number one had a unsurmountable unfair advantage effectively means,
that he had held the effective #1 spot for several decades. And its not like there hasnt been competition for it. Hero society is fiercely competitive.
All the top 10 spots carry a massive amount of prestige.

So no, Endevors position is just as solid as im thinking. He has a massive organisation behind himself, the leading hero agency in the country.
And i think its naive to believe having been #2 for so long means he isnt used to intense press scrutiny. Yes he has some personal flaws.
But yes he is also aware of them. Simply limiting his contact with the press handles a lot of those.