And the usage of katakana in the way the parent describes isn’t “tiring.” It follows almost the exact same pattern as words are italicized in English, where a word or phrase is represented differently from the surrounding text. Less common/standardized, but not tiring.
EDIT:
My bad on the bouten/dakuten confusion. Apologies.
Their point about katakana was also correct - normally a word is either written in katakana or it isn't, regardless of emphasis. Using katakana for emphasis happens but it's not common, and would get tiresome very quickly.
https://ja.m.wikipedia.org/wiki/圏点
As for katakana, it really does depend. For common or short words, people usually don't have a problem, but if you throw a whole katakana sentence at a Japanese person they will often stumble and reading speed noticably decreases.