The 'power' of impeachment without control of the senate has proven to be just a mild public shaming. As we've now seen, if the person you're impeaching (and the party that supports him) is shameless impeachment is about as useful and effective as wagging your finger at an axe murderer.
The House's exercise of its impeachment power is highly political.
The Senate's sole power to try all impeachments does not mean that it HAS to do so.
Even if the Senate directly informs the House that the Senate will not try or will try but lacks the votes to convict, in every case the House ought to proceed with impeachment if it concludes it is warranted.
Impeachment alone registers grave disapprobation.
An untried impeachment is not the equivalent of an acquittal.
The infamy of impeachment's "I" will always be an indelible mark in the history of the impeached high official regardless of the Senate's refusal to try them.