You and republicans don't get to determine how the House goes about impeachment. Just like the dems and House don't get to tell the Senate how to conduct the trial. Furthermore, House committees have the power to issue subpoenas, and only the enforcement of subpoenas has to have full House approval.
You're making the defense's point as it relates specifically to impeachment proceeding/requirments. The house at the time of those subpoenas had not approved anything related to impeachment. NOTHING. There had been no legal authorization given to schitt's committee to have impeachment related subpoenas issued or investigated. Trump was not legally obligated to answer impeachment subpoenas when impeachment had not been approved by the house.