I have done the following.. In vector tile style editor choose the map you want to remove labels from.. Save it as your own style. Then on items page, download the style.

This will give you a root.json file. In that style you need to add "visibility": "none" to all of the "label layers" I was using the World Navigation Style and I noticed that in the label layers "layout" all of the layers had "symbol-avoid-edges": true, I did a search and replace on the root.json file to replace all instances of "symbol-avoid-edges": true, with "symbol-avoid-edges": true,"visibility": "none",

then back at the items page I just updated the item (update button) with my modified root.json.

This removed most of the labels... still have labels for "Openspace or forest/label/Default" as that was the one label layers that didn't have "symbol-avoid-edges":true,
If you can find a string to replace in the style you want to modify, search and replace is much easier.
mark