The tiddly hats usually have a tiny strap that can easily be hidden by the hair (edit, or have a hair clip on the base). Otherwise they'd fall off every five seconds.
If they were their real none transformed selves it would be loli - but I guess it doesn't warrant a tag when they look older?
Well, in this one Lala's all untransformed and pretty loli-looking, but that didn't get the Lolicon tag either. It could be just that nobody suggested the loli tag for that one and the mods didn't bother.