Pelosi should've held a vote on starting the inquiry and gotten Republicans on the record. She's made one stupid decision after another around this process and will continue to make them until, or if, it gets passed to the Senate.
Had she held it right away every republican would have voted against it and then their positions would be locked in and very difficult to change. She can hold the vote whenever she wants but as things get worse for Trump and more layers of corruption are exposed it makes those votes worse and worse for Republicans.
Your idea is terrible. She can have them on the record whenever she wants.