You think drafting impeachment charges is productive? It's literally a foregone conclusion that the senate will acquit. The house knew that going in.
I don't know that we can say that definitively. It would only take a few Republican senators to join the Democrats to invoke using a secret ballot, and if that happens then the vote to convict becomes a whole lot more interesting.
This is purely a political play and the democrats think it will help them in the next election.
Not sure that that's true - Speaker Pelosi had to be pressured into letting the impeachment proceedings take place at all, since she thought it was the wrong move. She's been (at least publicly) very reluctant about the whole thing.
It will be interesting to see if their gamble pays off. Because it's just as likely from my perspective that it might end up backfiring. But don't think for one second this is about doing what's right. If that were true, sure, I'd agree doing what's right is productive even if you know it won't bring any results. But that isn't what this is about.
I think whether or not it's morally right (which by my reading is how you're using "right") is irrelevant. The Democratic majority in the House was voted in on a wave of very strong anti-Trump sentiment, so it could be argued that the Democrats are doing right by their constituents by impeaching Trump. If I had a Dem representative I know I'd want to see his/her name on the list of Yea votes, since that was my primary motivation in voting Dem in the midterms.
Also, not sure if you didn't see this or just didn't want to remark on it, but in case of the former:
Out of curiosity, what do you see as the Democrats' agenda? And the Republicans'?