Drizzling helps when undersampled. I have found it to be a significant benefit, but I am a pixel peeper and those of my images are intended to be viewed by pixel peepers. There are some trade-offs, but I do it every time under the conditions and the objects I am working with.
Why not drizzle the stars? In my rigs, where I use drizzle, the smallest faintest stars are sometime 1, 2 or 3 pixels in extent. If you like your stars looking like little boxes and “L”s then don’t use the drizzled stars. When I drizzle, those stars yield nice simple psf forms. They actually look like stars (photographic stars). And no, simply up-sampling a non-drizzled star field will not be the same.
However, even with very undersampled data, but with a very widefield intent, such as a widefield lens for landscape astrophotography, I really see no point in drizzling. At that point, the drawbacks weigh in favor of not drizzling. And if you want to print large, the the shape of the stars do not matter. It is the overall impression of the full field that is what is important.
Now for images that are not undersampled, I have also tried drizzling in that case. I will say that the drizzling absolutely did not improve detail resolution. However, I still felt that the star forms were much better and in the cases where I needed that, then I used it. Otherwise, no.