If the Senate refuses to have a real trial why should the House send the impeachment over?
Given that Trump will be acquitted in the Senate no matter what, the whole point of the House proceedings should be to gather as much information as they can until they have exhausted all resources. Democrats want to be able to make the strongest case possible for impeachment, and barring removal, they want to establish that there was wrongdoing so egregious that it hurts not only Trump's reelection chances but also the chances of any Republicans in competitive seats who defend him.
https://www.washingtonexaminer.com/opinion/if-democrats-dont-like-the-way-mcconnell-is-going-to-run-trial-they-shouldnt-rush-impeachment-through-house