I have a newer shop vac from 2016. The big one with the bar handle and large wheels. I use the filter and the bag at the same time. This is what the manual states to do as well as shop vac's instructional videos. Know why? You're picking up large and sharp debris - wood splinters, nails, screws, bits of metal, you know...in a shop...and guess what those can do to a paper bag? Yes, puncture it. What happens when your bag gets punctured? Yup, dirt everywhere.
The filter is extra protection in case your bag punctures. It also keeps the vacuum bin clean, the motor safe, and the vacuum not exhausting stinky air. Contrary to what you might think, Shop Vac motors are NOT protected for water and grit ingestion. Fine dirt will get into the motor and bearing channel and destroy it. Leaving water sit in them or sitting damp, and being run without a filter is the #1 killer of shop vacs.