Every school my kids have attended so far is neither truly progressive, because kids have very little choice in what they do, nor truly traditional, because the academic content is so weak.
Even curricula that are marketed as "progressive", like Trailblazers Math, contain all the worst aspects of traditional ed: bad homework, scripted lessons that kids are relentlessly marched through, and authoritarian pronouncements on how problems may be solved (no standard algorithms!)
It seems to me that the biggest stumbling block that prevents schools from achieving true progressive ed is simply this: control. To be truly progressive, to allow students as much freedom and autonomy as possible, just goes against the grain for educators. School is a place where kids are told what to do.
The biggest stumbling block that prevents schools from achieving true traditional ed is a pervasive lack of interest in real content. Professional-class parents are often more concerned about college admissions than learning. Too many educators don't know what real content looks like, and mistake activity for engagement.