What you were talking about is Congress essentially becoming President. Congress telling the President: Do this, or we try impeaching. Don't do that, or else you're gone from office. In that scenario, you have essentially done away with the entire executive branch, and just given that power to Congress. So no, I'm not for that apporach.
It shouldn't be clear what checks they are willing to carry out and under what circumstances, instead of leaving what would otherwise be very unclear? Why does making that clear automatically make it intimidation? Regular laws applied to citizens are made fairly clear to the rest of us.
To use your analogy of regular laws and citizens. What you're talking about doing would be like the FBI arresting a bank manager of a bank, for issuing a loan to someone. You're talking about punishing someone for doing something they have the LEGAL right to do. The President has the LEGAL right to pardon anyone he sees fit to pardon. Period. You may not like who they have pardoned, but they have the RIGHT to pardon whomever they want. I certainly didn't like Obama pardoning the traitor Chelsea Manning. But even I didn't suggest that Congress threaten Obama with impeachment over that pardoning.
True, some countries do have a system of government like that. Just like some countries put people who cross their borders illegals in prison for a very, very, long time. But that's not the system of Government we have here in America. The Founding Father's made it clear, they wanted 3 branches of Government. They didn't want an all powerful executive branch, which is why they gave Congress the power of the purse. They wanted checks and balances. But checks on another branch of Government is not threatening the other branch to do what you want. That's not a check on power, that is usurping power. Big difference.