You may find you need hard copy "working documents" for some things that can be recycled when no longer needed, so long as everyone and I mean everyone in the organisation has instant access to the full range of documents there is no need to print everything out to have a hard copy.  It is vital though to set a watermark on the documents so that if they are printed it is obvious that the document is out of date

BEWARE share point - if it gets deleted the bin can by default have an automatic self cleanse after 30 days!

We use share point across two libraries one that everyone can access where we only store a locked pdf of the current document and a second with limited access to the editable and archived versions.

Within a library you can assign user groups so for example supervisors can view and download to print but not delete or edit. Their manager have editor rights so when they update a document they can drop the new version in to the library and move the previous version to archive.

We add a header to every document showing its version and date - if someone has a paper copy e.g. in the warehouse the leading hand can easily check the hard copy against the electronic

I understood the question to be about the need to keep paper copies of documents.  I don't think it matters whether the electronic version is on Sharepoint, the Intranet or any other method. 

I think there will be three main reasons to have a paper copy of a document:

1. If a paper copy is required to manage a process.  For example, issuing a paper Permit to Work allows individuals to physically sign on and off (although fully electronic systems are available). In this case the paper copy could be destroyed once it has served its purpose.

2. If people may need urgent access to a document.  A good example would be an emergency procedure, especially is loss of power is a possibility. In this case the paper copy must be subject to formal document control processes.

3. There is a legal or other requirement (e.g. contractural) to keep a hard copy of a document.  I know in the past there was a perception that this was required for things like Permits to Work, but I am fairly sure that using a recognised document management system like Sharepoint would mean this is rarely required.

To answer AK's comments.  One of the features of document management systems is that they allow people with the appropriate permissions to check out documents for revision and then check them back-in after update.  Document users will typically only have access to the latest, approved version but the system stores all versions so that a full audit trail is available. This really should be an improvement on past systems where people would have had various copies on their own hard-drive etc. but does require some behavioural changes.