When banks and such started making it possible to download statements, I began doing so, mostly because it's a lot easier to store and find PDF files than paper ones. At least for me, I can locate a particular document much more easily if it's on my computer than if it's in a file cabinet someplace in the house. And of course, it takes next to no space to save PDF files vs. paper. However, I still find it easier to peruse a paper statement to see if anything unusual appears.
Now banks and stock shareholder agents (e.g., Computershare.com) are getting more forceful in their efforts; more and more I'm finding I no longer have access to the downloadable statements unless I agree to forgo the paper version.

How about if they give me a nominal fee, like $5 per quarter to forgo the paper statements? Fat chance. Another example of big business thinking we're all idiots.