Can we use scanned EOBs instead of keeping paper copies?

This is accepted practice. Indeed, it can be better because you can actually find scanned EOBs if you are ever audited, unlike most paper EOBs. 

The relevant legal issue revolves around admissibility, I believe. 

According to ruling Rev. Proc. 97-22, the IRS allows one to prepare, record, transfer, index, store, preserve, retrieve, and reproduce books and records by either electronically imaging hard copy documents to an electronic storage media, or transferring computerized books and records to an electronic storage media that allows them to be viewed or reproduced without using the original program. 

According to ruling Rev. Proc. 97-22, the IRS permits the destruction of the original hard copy books and records and the deletion of original computerized records after a taxpayer completes testing of the storage system. 

By all means look into state laws, but many practices are doing this. 
