Note that Shannon did use the word "alone", implying that commissions is not the only reason why this strategy is not as great as it seems at first. I'm guessing he (being one of the most prominent mathematicians of the 20th century) picked this example exactly because it was a counter-intuitive and complex problem that seems simple on the surface.

It would still apply. Them taking a percent of my money every trade hurts me. Is there any guarantee that my profit per trade is larger than their fee per trade?

You pay the same amount in fees for buying a lump sum of $100 in Bitcoin or for buying $100 in Bitcoin over a week using dollar cost averaging. If dollar cost averaging with no fees is better than a lump sum with no fees, then I'm not sure how adding the same fee to both strategies could make dollar cost averaging any worse relatively.