A doppleganger of Star would be extremely useful for putting Toffee at a disadvantage to find the real Star.
I'm not sure that we should be putting too much stock in how well a doppleganger of a dead celebrity will boost our reputation, though. While they'd probably boost our public perception somewhat, the QMs have mentioned that people's opinion of us is more complicated than a sliding scale and that doing things people like doesn't make them forget things that damage our reputation.
Right now, the big negative thing about how people percieve us is probably that we're irresponsible. Which, to be fair, we are, because it's in character and makes for a more entertaining story. We did research into Flubber, we carelessly gave LOVEMUFFIN carte blanche to rampage through town, we routinely fire off Inators that inconvenience people, and DoofOS's flaws have been going unresolved for months (not for lack of trying, but the average consumer is unlikely to be aware of how much effort we've been putting in). Building a robot Mr. Rogers or Elvis will be appreciated, but won't do anything to change that perception.
I believe that our best bet for improving our reputation would be doing stuff that provides solid, tangible benefits to society. Curing genetic diseases, for instance, and pursuing Greevil tech. Dinosaur parks and robot celebrities are fun, and they remind people that mad science doesn't have to be harmful, but I think that people seeing us make an effort to improve society instead of just distract it will be better for our reputation in the long run.
Additionally, considering how closely our name is tied to Toons, we might not want to have a reputation for "entertaining, but obliviously detrimental to society".
