There’s no “suspension of pardon power”. The “in cases of impeachment” clause means that a President can’t pardon someone else’s impeachment; e.g., can’t pardon the impeachment of a Federal judge who has been removed by Congress and put him back on the bench.
The courts will have to address this very argument when the time comes, and most certainly, those seeking to validate their claims to immunity for their crimes will be seeking judicial relief right up to the SCOTUS.
Impeachment is like an indictment. From the Framers' point of view, would it make sense to indict an official for treason, bribery, high crimes, etc., and allow the accused to continue handing out immunity from prosecution to all his partners-in-crime during the proceedings?
Flatly, no.
In a better world, with a less corrupt House and Senate, and media, impeachment could be done in the morning, and the Senate could convict, and remove, and bar from any future office, in the afternoon. Especially, with the long, long list of offenses now being publicly discussed by Ted Cruz, the House investigators, the governors, etc.
The media are hesitant to report anything because they too have been threatened to remain silent. Time and pressure. Little cracks in the dam; little trickles of water; eventually, the dam will give.
Clinton's only impeachable offense in the beginning was trading nuclear and guidance technology to China for campaign cash. Bob Barr submitted the bill. It was too drastic; too serious. So they went after Clinton for stains on a blue dress, lying under oath, and obstruction of pornographic headlines, essentially.
This administration has waged economic and political war against the citizens of the USA like nothing the world could have ever imagined. It will only get worse during the next two years. Congress is probably doing the right thing to officially deny that impeachment is the objective, while the discussion of impeachable offenses is spurting out through the little fissures all across the face of the dam.