In that case, the traditional uncountable nouns aren't uncountable. They're singular.
Yes. For me, at least, all uncountable nouns are by definition singular, conceptually speaking, because they cannot be divided up. That doesn't necessarily mean they're all singular in form.
The news is on. [plural form, singular concept]
*The news are on.
It's the conceptual sense of plurality that governs, say verb agreement, which is why we can say things like:
The police are coming. [singular form, plural concept]
ps. Swan (2016. §120.50 notes;
Some uncountable nouns are plural. They have no singular forms with the same meaning, and cannot normally be used with numbers.
I've bought the groceries. (BUT NOT ... a grocery. OR ... (three groceries.)
If you're going to say that 'groceries' and 'clothes' are uncountable, I think you should mention by what measures you're talking about. This becomes an academic question of definition. What is countability? Some people think that if something is not able to be counted into one, two, threes, then it can't be countable and therefore must be uncountable. I wouldn't go along with that.
Some words just don't fit neatly into either count noun or non-count class. The word
clothes is one of these problem words. You can have 'many clothes', but not 'much clothes', and you can't have two or three clothes. That's a problem for classification.