Founding the NHS, bringing in clear air and water acts, regulating minimum standards for child workers (and then all workers), extending the franchise. All these were done in defiance of precedent and with strong accusations of destroying prosperity.
The creation of the NHS is a good example. Nothing had been done like that before, and most of the predictions (both positive and negative) at the time, were very wrong (for instance, it was predicted that it would reduce medical costs overall!). This strongly implies that nobody really had any idea what was going to happen. And yet it basically worked out; and, in fact, most healthcare systems in developed countries (apart from the USA) seem to average out around the same broad categories of performance and cost, even if they seem to vary considerably in theory, This is evidence that our current systems push both revolutionary innovations and incremental ones, in the vague direction of decent performance,
On another side, many technological innovations completely destroy Chesterton fences existing in society. The whole idea of centralising and sharing knowledge across all different types of communities is something that there were a lot of fences to block; yet it seems to have kinda worked.
But the proper argument would require much more examples, and much defining of what a Chesterton Fence is.
For the Chesterton's Fence objection to properly have applied to the NHS, it would have had to have been the case that no one could explain the historical lack of NHS. Yet I think it's pretty easily explained by governments' values over time: first kleptocratic, then libertarianish, and only becoming utilitarian roughly around the time of the NHS, to simplify heavily.
Chesterton's meta-fence: "in our current system (democratic market economies with large governments) the common practice of taking down Chesterton fences is a process which seems well established and has a decent track record, and should not be unduly interfered with (unless you fully understand it)".