Yes, but that would still make such a product less marketable.
Let’s go through the issues with mass marketing such technology. First, we have to figure what the cost would be to develop the product, and then to produce and install it. I don’t have a number, but it would probably be expensive on both ends.
Then we have to figure how many people would buy it. I don’t specifically know that either, but we can eliminate many. We can eliminate anyone who has a dishwasher. We can eliminate anyone who has two sinks. We can eliminate anyone who, despite having one sink and no dishwasher, doesn’t generally leave their dishes to pile up. We can eliminate anyone who is uncomfortable with washing milchig and fleishig dishes together in hot water, one factor being that it’s not l’chol hadeios.
Figure that most homeowners have either two sinks and/or at least one dishwasher, and figure that most people would probably not invest the hundreds of dollars it would probably cost into a rented home.
I think there’s no money to be made on such a product, so nobody developed it. Shabbos clocks, on the other hand, are not even a specifically Jewish product, and they serve a more important and widely useful function. Even the Kosher Lamp, which is marketed to shomer Shabbos people, is more useful, and more affordable, to a much larger group of consumers than would be a kli shlishi sink, in my opinion.