In general it is more cost effective for both payors and payees to use the electronic format for claim submission. In addition to the push to 837 submissions, the trend is toward 835 (remittance format) because it saves the payors money.
All clearing houses will support paper claims.
The question is more about if and when a practice opts to submit paper.
We submit CMS 1500 to Medicare because it is cheaper for us to do so. Office Ally charges a flat fee of about $20 per month if the ratio of governmental claims (Medicare/Medicaid) to commerical claims exceeds 50%. It costs us no more than $8 per month to send the paper claims to Medicare. The longer response time and slower cash flow are not issues for our practice.
Certain very small insurance companies will not accept electronic claims, hence no choice but to use paper.
There are usually one or two pesky claims which will require paper to resolve.