i received a message regarding this thread.

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first things first: it's not true that comparison words MUST appear in tandem with "than"; they can certainly appear by themselves, too, if there's enough context to make their meaning clear.

here's an official problem (gmat prep) on which lots of different comparative words appear without "than":
https://www.beatthegmat.com/minivans-car ... 09996.html

i think the point here is just to make you realize that you can't substitute another word for "than".
for instance, you can't write "more X compared to Y", or "more X as Y", or whatever.

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regarding the sentence in the example: yeah, you should probably have an explicit time comparison.
you don't need all of the extra words that are in your examples -- for instance, it's ok to write just "i will have higher bills this year than last" (see also OG12 #93) -- but, yes, you should have that comparison in there.
the authors of that example probably just weren't thinking about that particular issue, because that's not what the sentence is meant to illustrate. (if the sentence were part of a larger context/paragraph, it could be ok without explicitly containing the time comparison. since people don't generally think up sentences completely in isolation, that's probably why the authors didn't include an explicit time comparison.)