This is mentioned in the article, but it's a small piece in a paragraph so understand why it could be missed:

"Somebody thought IV was not easily understandable because it resembled VI..." (in paragraph 2)

I have always believed this to be the reason.

semi literate populace did not have watches though...

Clocktowers on the other hand...

The way I read a watch ignores the numbers anyway (arabic or roman) and I know where 9 is etc.

if the device is upside down it is evident and I don’t even try to read it, I right the clock or take off and restrap the watch.

So why would IV and VI a problem and IX and XI not?

Maybe because IX and XI are not upside down, only at most 90 degree angle.

Hmm... I'm skeptical that anyone able to read a clock in the first place would be unaware that 4 comes before 5 and 6 comes afterward.

Indeed - I have always thought (though I don't know if I was told this or just made it up) that IV was used, in general, over IIII because the latter could easily be mistaken for III, but as clock numerals are on a circle, dividing it into four equal quadrants, having a numeral of any sort gives very little additional information over a simple dots, pips or tick marks.

So why use a numeral at all? Well, there's always those people who will think that it is obviously wrong not to have numbers on a measuring instrument. Also, in early modern times, clocks were expensive items and expected to be ornate, especially as they were not all that good at keeping time.