State laws vary, CA, MI, etc. The ATF doesn't have a number attached to the barrel length of a "pistol," therefore a lot of states who simply have no wording in the law allow 16"+ barrels.
This comes in handy in a state like MO where the Alternate Season opens with no rifles allowed, but an AR pistol with 16" upper (from the hunting AR rifle) is legal.
YMMV! State law is the final hurdle.
Goes to possession and carry, too. Some states allow loaded concealed carry of a pistol close to hand in a motor vehicle, but a rifle must be cased unloaded in the "trunk" of the vehicle. That's the situation in MO, maybe not for others.
Another provision of pistol vs rifle is that an SBR must have ATF permission to cross state lines. It's reportedly a simple form to carry when approved for a one year duration. And you have to jump thru that hoop annually.
Some do, because common knowledge says that a stock on the buffer tube is for some reason "better." I've read a lot of comments from owners of pistols who then SBR them with a stamp and a stock, but none report the actual MOA improvement they gained for the effort. They shot them both ways, unfortunately the reports are largely glossy positive comments with no substance. It raises the issue that the tax stamp is being defended more than the MOA improved.
The gun itself can be identical in every other regard - the only change in operation was adding more vertical surface to place against the shoulder. For the $200 of a stamp, or $125 for a brace, I don't yet see where it accomplishes much. It is, after all, an AR15 with little recoil to begin with.
There are more issues with "pistol" vs "rifle" in a build. I definitely agree that under the current interpretation building a legal pistol first is preferred for the follow on options later. If that is the case. then turning it into an SBR negates them almost completely. Once an SBR it's a tough row to hoe getting it back to being a legal pistol, and use and carry seems more limited, too.
Food for thought. Consult your state's laws. It's not a blanket answer for everyone.