So, I've been a bit sluggish to take up
@onering's challenge here. Have been operating on too little sleep to feel comfortable in my reasoning. Now that I feel more able, I'll see how well I can explain my position.
So, first off, I do think having a number in common with another format is helpful, in that it's easier to remember one relatively arbitrary number than to remember two. And it means nobody needs to keep track of "wait, which format was 5 and which was 7 again?" So that's an advantage over numbers like 5 or 10.
So why a middling number, rather than, say, 3? For me, this boils down to wanting people to include
more niche pet cards, over feeling obligated to make primarily value choices. I think somewhere in the 5 to 10 range is a pretty good number for this specific purpose. Contrast this with charms, where having two of the options being super niche basically kills their usefulness unless the third mode is worthwhile all on its own, and note that here, if one option is sufficient to carry the build-your-own charm, you may as well just run that in the maindeck. So you can have one niche pet card at most with three wishes unless you're actively weakening your deck for the sake of options that you usually won't even get to show off, which might be a tall ask for a lot of people. I expect three card wishboards to be filled with "value" plays a lot, rather than interesting obscure cards that we don't really get to see very often.
Now, the point has been raised that niche cards can mean, for example,
Rest in Peace or
Tranquil Grove. I don't see this as a particularly large problem, but perhaps more importantly, they can also be things like
Blood Reckoning,
Cower in Fear, and
Mindclaw Shaman. I have a number of pet cards that I quite like, that I jam into decks despite them being outclassed, and that I would like to fit more of in my decks. I would like to see more people playing obscure nonsense in creative ways. This, for me, is the primary upside of Wishes, and I think it would be lost by restricting the Wishboard to 3 cards.
Meanwhile, on the other extreme, unlimited or functionally unlimited Wishes could very easily also undermine creative deckbuilding. "Restrictions breed creativity" is definitely true, and some meaningful restrictions will encourage people to select a handful of cards that fit the deck's concept during deckbuilding, rather than grabbing whatever fits the requirements at the moment in time when the wish is cast.
TL;DR --
The reason I have for desiring Wishes to be a thing is to carve out a niche for cards that are just not worth playing 99% of the time, but which are fun/interesting/flavorful, rather than relying on the existing most versatile versions of the various effects which are often far less amusing and fit the flavor of a Vorthos-y deck far worse. For those specific purposes, something in the range of five to ten cards is the most reasonable, and given on top of that that there is precedent for seven cards in specific, I think that it is best to adopt the same number for ease of remembering.