I'm not sure how drizzle can be viewed as a blurring algorithm. While it isn't exactly a sharpening algorithm either, it does recover information lost to sampling and the net effect can be a more detailed final image. The amount of detail that can be recovered is directly related to how undersampled the image scale is.
I agree with you. As I stated above, I used to Drizzle most of the my images from my refractors at 1.19 and 2.02"/pixel image scale. For the shorter focal length, I still drizzle since it is the most undersampled and the widest field. My APOs have been down waiting for a part for my new focuser so I have been mostly imaging with my SCT at 2159mm F/L. For my SCT at 0.36"/pixel, Drizzle make no sense at all and this is why I started to do MUREDenoise. I spend a bunch of time figuring out how to make it work and now its so good, that I dont want to NOT use it. When you do MUREDenoise and a good DBE on the master frames first, I fine the Deconvolution is both easier and significantly more effective with much few artifacts. This make sense because of the different length scales that Deconvolution and MUREDenoise work at. Two of the big issues with deconvolution are
1) that you have to be careful not to over do it since you sharpen the noise too much and get ugly background even if you protect it - especially in the no mans land between the bright and background portions of the image. Since MURE Denoise kill the noise across the image and not just in the background, you can get more and better quality sharpening without the ugly artifacts.
2) it can take many iterations to find the right global dark and global bright setting for deconvolution. What I have found is this is much easier and I end up using that same setting for just about all images. I test it to be sure, but it just seems to work.
I have gone back to my APO data at 1.19"/pixel. It is marginally undersampled. You can see improvement with drizzle for sure. But I have found that the combination of MUREDenoise and a good deconvolution leads to a significantly better result overall. I have even now gone back to old data sets and regretted that I did not keep the non-drizzled masters.
This is just my opinion and experience, but I highly suggest that you try it. MUREDenoise takes a bit of effort to learn to use, but much less that Deconvolution took.