I don't know of any law professors who would take that extreme view, that Trump couldn't serve as president via natural succession from a position other than vice-president.
And that would be my rebuttal to the calheel "elected has to have some significance." The limitation closes the VP loophole because of the 12th. It isn't true for the speaker of the house. There's just no way to interpret the provision rationally to prevent the Speaker loophole. Note that the line of succession is itself of questionable constitutional validity and there are influential people who think that no legislator or the speaker can succeed to the presidency.
It's not true that the drafters never considered a scenario like this. They didn't spend much time on it, but it was mentioned at least a few times during the debate. Enough to show that it was a foreseeable consequence. I also think the "intent" is not as clear as you think. When you look at the history, it's messier than that. Truman's status plays an important role.