I don't use a wallet myself preferring a small box, but thats just personal choice. The above look good and I'd rather fancy the wooly side of sheepskin to work well for keeping and releasing ones flees, without affecting future keeping properties of the retaining material, unwoven wool I'd think perfect.
I've different boxes for different flys used for different types of fishing and situations, running water, still water, sea trout brown trout salmon etc. So it depends where I'm headed as to what I'll take. I don't think one can have too many flys if one limits one's self to a single small box or wallet, perhaps two, eg wets and drys. If one finds oneself with the wrong flys one learns and adjusts the selection accordingly.
I think sea trout fly fishing is about the most minimalist of my fishing when it comes to fly selection. Even then the minimum number I'd consider viable for an hour or two would be; one for the bank, one for a tree (sometimes two depending on the spot), one for the submerged snag (remember to recover the mono) one to blunt and a couple to get roughed up by trout teeth. Then a duplicate number in a different pattern (depending on light conditions, dark dawn dusk dull bright etc, or water levels and water colour if daytime fishing a spate). So, around 12 in total for fishing known bits. That said, I'm usually not far from the car when doing this type of fishing so I can always nip back for a top up or different patterns if I've miscalculated conditions
Casts (tippet for those in the south) I carry on the spool in my pocket and make them up as required. Sod's law dictates; if you pre make a cast it'll be the wrong one! Better to take bare mono and make them up as required, unless I'm fishing in the dark.
So, I personally have a need for a few small boxes/wallets to keep different selections in, doesn't mean I need to carry them all all the time.