As someone who has been drawing a ton of sidewalks and crossings lately, this is probably the most annoying thing I have to encounter. You can get around the warnings for marked crossings that are automatically created by just setting the markings, but you don't have that option for unmarked crossings so you either have to set the tag in bulk at the end or hit the upgrade tags button on every node.
This has to be an easy fix to send in a pull request... 🤔
You can select multiple entities at once by holding SHIFT while clicking them (in iD and JOSM at least). From there you can set the missing tag (I think it's marked=no) at the bottom of the combined tags table in the left pane.
Ah, but I'm doing edits all over the map. Selecting 50 crossings is tough when I don't remember which ones I've done this session. They should really just fix this bug.