Can Impeached presidents still perform pardons?

All that the pardon language in the impeachment provision means is that a president can't use the pardon power to undo an impeachment.

I wonder what makes impeachment so unpardonable?

To me, it makes much more sense to remove that power from an impeached president.

Like, murderers, serial killers, terrorists are all eligible for pardons, but someone who has been impeached is a bridge too far?

Very odd, to me.

The Act of Settlement of 1701 imposed for the first time a limitation on the power of the King of England to grant pardons by providing that the pardon power did not extend to impeachments. Presumably, this step was taken by Parliament to protect their impeachment power from being undercut by the action of an unelected king (or queen).

Thank you for taking the time to explain the origin.

Although, it still doesn't make sense in today's context, but such is often the case with laws.

by the Senate, he is still the President, and can still exercise all of the functions of that office.

Most elected officials under indictment are allowed to work and have full job duties.