Doing away with the Senate would be change to the fundamental agreement that was made when each state joined. The only moral way to do it would be to dissolve the existing United States and then let each of the 50 individual states decide if they want to remain as their own independent country, join the newly formed United Residents of America, or join some other country, perhaps Mexico, perhaps Canada, perhaps one of three or five new countries formed out of collections of the 50 states that used to be part of the United States. Simply removing the power of the individual states that they were given in exchange for joining the Union is immoral.
What makes you say that morality demands accepting the premise that states are the fundamental unit, here? That is, even acknowledging that the people who signed the constitution imagined themselves to be acting on behalf of the [landowning male] residents of their states, why are we morally bound to adhere to their model of political authority?
Also, the Constitution itself provides a different avenue without dissolving the union, so it can't simply be a matter of invoking the original agreement—which would beg the question I'm posing, anyway.
(I'm not expressing any agreement or disagreement with your claim, just its support.)
>why are we morally bound to adhere to their model of political authority?
We're not, the Constitution can be changed, the government can be replaced, you can go somewhere where government works differently.
The philosophical ideas behind some of the "unfairness" of the Constitution were good ideas and have led to a lot of higher-level fairness which people tend not to appreciate.
We're also just the longest surviving government in the world besides some very small exceptions, so apparently quite a few things worked.
What's immoral is that I'm forced to be governed under an unfair agreement that I had no say in accepting. Giving some people more votes because they live in a different state is absolutely immoral, agreements change.
You vote, you didn't leave for somewhere else. How can you otherwise consent to being governed without you individually being in charge? There are people who would think how you want things to be governed to be unfair, how do you reconcile that?
I think it's a fundamentally flawed system and it's telling that the numerous times the US has had a chance to setup a new government in the aftermath of overthrowing the last one we've always as far as I know go with the good old parliamentary system of some flavor.