For partly the same reasons as you posted, I think we generally have better Presidents if they either come from Congress or have served as governor. To me, it's important that a President accept that he's not king-of-the-world and needs to work with people to get things done when acting in a government role. It doesn't matter so much if Presidents are actually trained as lawyers or not.
FDR, Carter, Reagan, Clinton and Bush Jr. were all Governors. As Governors (and as Presidents), they did not always get their way and had to adapt accordingly. Some of them were good and some were not so good.
The only recent Presidents I can think of who were not Governors or from Congress were Eisenhower and Trump. However, General Eisenhower previously dealt for at least 6-7 years with politics (think Roosevelt and Marshall) and getting along with competing interests of powerful pricks (think Patton, McArthur, Montgomery and Churchill), plus operating on a limited budget and limited supplies coming to him from 3500 miles away.
That leaves you-know-who, who never worked in government, who inherited a non-corporate family business that never required him to learn how to bargain with adverse opponents (like boards of directors or shareholders) and whose signature negotiating tactic is to threaten to walk away from the negotiation if he doesn't get his way.
His paramount campaign promise in 2016 was that, on his first day in office, he would demand he be presented with legislation to immediately repeal and replace Obamacare with something better.
The president claimed Friday that he hadn't promised such quick action.
abcnews.go.com
He never came close, because he never accepted that Congress can't act that fast, that a President has no power to enact laws and that walking away from negotiation doesn't do a President any good.
Love him if you want to. But Trump doesn't know how to give you the government his supporters say they you want.