I want to emphasize that avoiding the score adjustment is not a design goal of this system. The point of the adjustment is to allow entries to be relatively ranked in the bottom half by minimizing the randomness factor by scaling down scores with lower levels of confidence.
It is not, but I believe enforcing the score adjustment isn't a design goal of this system, either.
The problem with the current system is that even if everyone puts at least close-to-median-sized effort, they still might get their score adjusted semi-randomly, with some entries getting one or two ratings below a median of, say, 20 (just like rolling a 6-sided die 60 times doesn't mean all numbers will appear exactly 10 times). It can lead to a somewhat ironic situation, where the system designed to minimise the randomness factor introduces another randomness factor (i.e. which entry ends up with an adjusted score and which won't). After all, using median means that - excluding entries with exact median number of votes - the lower-voted half of entries will get its scores lowered no matter what.
Also, while the median increasing by 1 might not be significant with a median of 100 votes, the score adjustment might be more significant with a median of 20. And considering median depends on how many games can people play within voting time (as opposed to number of entries), I'd wager getting something like 10-20 median across 200 entries wouldn't be all that unusual. With medians this low, the randomness factor of score adjustment becomes particularly prominent - possibly even moreso than the few-votes variance it's designed to minimise.
Another randomness factor comes from the indirect relationship of giving-receiving - some people might get lucky and get 100% of reciprocal votes, while others might often give their feedback to people who aren't interested in voting at all. Not sure if itch.io more prominently displays entries with higher "coolness rating" (i.e. how much feedback the author gave vs how many votes their entry received); it would definitely add a stronger cause-effect in the giving-receiving relationship.
On the other hand, I imagine public voting would add some extra randomness to giving-receiving, because there's no way to vote on a public voter's entry in hopes of receiving a reciprocal vote. I suppose public voting shifts relevance away from feedback-giving to self-promotion (the higher the proportion of public voters, the more self-promotion becomes relevant compared to feedback-giving). Not really calling to remove public voting altogether, rather pointing out another reason why voting for other entries might not always be the most effective nor reliable method of getting past the median threshold.
I do not advocate for 100% entries avoiding score adjustment most of the time. I do, however, believe that if I take my time to cast a median amount of votes, I should reliably be able to avoid score adjustment (say, 95%+ of the time). Thus, among the numbers-checking for the previous Jams, it might be worth finding out how votes given correlate with votes received. In particular, how much of median I'd be guaranteed to receive 95%+ of the time if I voted on median number of entries. This could give a more fitting median multiplier than my feeling-in-the-gut 80% I initially proposed (assuming my proposal would be implemented in the first place).