It’s the Senate that is the real problem, and not the House of Representatives. And so, since the House knows that it will never make it through the Senate, that puts a real big damper on any action in the House!
You, like so many others on FR have it backwards, cart before the horse, tail wagging the dog, etc., Etc., ETC.
By the Book: Arrest, trial, sentence.
By the US Constitution: Impeach. remove from office, punish. Got it?