Reasons to keep paper bills:
Paper Bills are useful to review in the future your past energy use, or quick look at last year's spending. They're good for proving address or Identity checks (you ever had to get an Enhanced Disclosure?). Or when you sell house, the buyer's soliciter will want to see paper bills for water, etc. So might someone compiling a HIPP.
Also easier to claim for damages, if it comes to that, if you have a paper bill (say for car or house repairs) that documents what was supposed to be done.
Or if you want to check in the future what foreign exchange rate you got last year using your credit card in country X, commpared to what is being quoted now.
Or imagine you find out later a mistake was made in how your mortgage payments were calculated, much easier to document if you have the actual document issued by the lender.
Also, personally I find looking at historical documents using paper spread out around me much easier than viewing one page at a time on computer, or having to print it all out again later, anyway.