Should presidential powers be stripped away during impeachment?

[President Johnson]

No.

Impeachment is equivalent to an indictment. The House merely sits as a grand jury & votes on whether to indict based on the evidence it collects & the case that's built. This requires a mere majority. But during the process, the President ought to remain in office (as they do) with the full powers accorded to them by the Constitution, in part because the American legal system assumes innocence until proven guilty; in other words, innocence until conviction. Unless & until the Senate has held a full-blown trial that concludes with a 2/3rds guilty verdict, there ought to be no official reduction in or limitation on the President's authority.

I was actually leaning towards yes, but that answer convinced me to vote no.

[President Johnson]

Actually it's a standard in many countries to have impeached President suspended, and I'm personally leaning toward this. Yes, as the previous posted pointed out, it's just an "indictment", but on the other hand it's pretty customary for people to take a leave of absence while on trail.

My only worry is that it could be abused by the hostile House majority, but that could be fixed with setting some rules.

This is the issue.  An opposition-controlled House would always make up a reason to impeach on day 1, and would also impeach the Vice President after they assumed the presidency, so we would likely end up with the Speaker of the House being acting president a majority of the time, rather than either of the people elected to the 4 year term. 

Well, in a healthy political climate, the House majority actually wouldn't. Today's Republican Party is a different story.