1) All House votes are by simple majority. [There is no historical precedent to raise the threshold]
2) Every member of the House serves a two year term. So there is a check 'n balance on their vote as they have to answer in the next election. Generally, only a third of the Senate is up for the next election.
3) Proving removal from office "beyond a reasonable doubt" to 67 Senators is a demanding burden.
There is some merit in Scott's proposal, particularly if the same party held a slight majority in the House (e.g. GOP 220 - Dems 215), but a stronger majority in the Senate (e.g. 62 GOP - 38 Dems). As a Democrat, one may fear pure partisan politics could run a President out of office on a bogus charge, only needing a handful of votes form the other party in the Senate.
But, that scenario assumes everyone acts in bad faith. I do not believe we are anywhere near that point.
If a President's misconduct gets > 50% of the House to impeach him, pretty sure it was warranted. The media is also a force to expose bogus charges.