The kind of stuff found in the Pepys and Roxburgh collections of broadsides from the late 17th century is indeed unsingable, at least by today's standards.
Maybe by period standards as well. Relatively few went into tradition (oral or otherwise), and it's likely that the vast majority were rarely (or never) sung at all - at least as printed.

And maybe were never intended to be. There is a recurring type of versified polemic which has a named tune, and where knowing the tune carries the ideas along, but which is far too long for any performance. Some of the best of these were by the Chartists in the early 19th century - I have in mind one tremendous attack on the alcohol industry from Northern England around 1840, when the temperance movement was entirely within secular social radicalism and was resisted viciously by the churches (who only picked up the issue a generation later). It's at least as good as anything the Wobblies did, but the guy who wrote it can hardly have expected all 40-odd pages of it to be sung out loud, not least because he was doing a long jail stretch for sedition when it was published.

Less attractively there is a shitload of page-long fine-print Jacobite rants from the early 18th century, which no doubt served a function as a memorable catalogue of grievances, but even the drunkest group of upper-class twats on a binge would have told you to STFU if you tried to air them in public.

It isn't an artistic failure if something like these didn't get into tradition - street directories didn't either, and you can sing them pretty well to psalm tunes.