The old dingbat will hold onto the articles of impeachment and this will fade.
It cannot work like that. What you are suggesting is that the House can try POTUS for impeachment, offer the Prez no opportunity to face his accusers or defend his innocence, hold secret hearings where only one party can submit evidence..... Then the House can just hold the Articles of Impeachment indefinitely thus declaring POTUS guilty and continuing to deny him a venue to defend himself.
GUILTY FOR ALL OF HISTORY!
No fair system of justice could accept that outcome - although the Demo'rats could.
In my view the White House should bypass the Senate and go directly to SCOTUS to declare the House process and the Articles null and void. That unimpeaches the president and discourages the Dem House of further planned destructive actions.