First, it was smost of the northern...American Baptist convention, that went worldly, and off the rails
Now it seems, the SBC is following suit. They have always done better it seems, as independent bodies, not beholden to any overarching convention.
There are independent Baptist churches, which still hold close to scripture...and many non-denominational churches are patterned after the historical and independent Baptist churches, which is not at all difficult, since they do their best to follow the Bible...Sola Scriptura..
I believe your idea is sound, since denominations are man made. In fact, believers were not even called
"Christian', until it was loaded upon them at Antioch. Earlier, some called them "the way"..