Cadw would have been consulted ... It's a devolved matter...
Well, yes and no. First of all, Cadw is a "trading name" of the Welsh Government so to speak, not a separate legal entity.
Most of the scheduling in Wales took place a long long time ago before the devolved government existed. Cadw, i.e. the government, decides what and if to schedule and the landowner concerned then has to react accordingly, and in turn their visitors. It's not done in the order where visitors ask landowner to get their land scheduled, then the landowner asks Cadw to schedule it, etc.
The full list of Welsh Scheduled Monuments where we have identified some underground mine or quarry or cave aspect is here:
http://www.cambriancavingcouncil.org.uk/pdf/newsletters/2018/historic-sites.pdf
The above list does not generally include those sites where it is the built surface features that are the scheduled objects of interest, such as the old quarry inclines or works buildings, as is the case at Aberllefenni, Bryneglwys, Rhiwbach and so on, because these things are not underground.