So why have they not held a full House vote on impeachment and instead are conducting an "impeachment inquiry."

Because of internal Republican polling, according to NPR's Susan Davis... she wrote that the National Republican Congressional Committee "briefed House GOP on private polling conducted Oct. 1-3 in 95 districts (55D /40 GOP)."

"Don't expect any cracks in GOP unity: memo concludes voters 'are much more willing to vote for a GOP candidate opposing impeachment than a Democrat supporting it.'" https://www.wnd.com/2019/10/de....ms-not-pushing-impea

Why Dems not pushing for 'impeach' vote - WND
www.wnd.com

Why Dems not pushing for 'impeach' vote - WND

Impeachment has been in the hearts, on the minds, and the tongues of President Trump's critics since before he even took office.