A nice idea but how does it work in practice?
Going paperless if you are previously used to using paper requires a big “mind shift”. You have to be super organised or things will get lost. Instead of sifting through mounds of paper to find something you know is there in a “safe” place, you now have to remember which computer folder you put it in. If you have gone slightly “off piste” with your filing, it may prove very difficult to retrieve a document you cannot find unless you have a rigorous method of naming files to enable a search of the computer to be performed. You also need to have a very active brain to be able to work on screen only with no reference to a printed sheet. However, a lot will depend on the type of work you do.
If you work in a team everyone has to be well drilled in the paperless procedures. It is no good someone misfiling something as that could be potentially the last you see of it! A huge amount of trust and training is required to make this work in a team and I believe this is why a lot of offices are not keen to take this option.
However, disciplined procedures should be aspired to in any organisation, so the transition to “paperless” should not be an issue. Consider the benefits: cloud storage of information, reduced stationery and storage/archiving costs, ease of access by the whole organisation. The pain of the change may well be worth the gain.