Hmm, I live in Poland and once I found a lost wallet (no money inside, so probably someone stole it, almost every one has some small cash there, at least coins) and my first reaction was to mail it to the person it belongs to, there was a national ID inside and I did that.
It never occurred to me to get it to the Police station. Probably because they never found my wallet when I reported it (and reporting it was a PITA, 2 hours of lot time).
10% of cash inside? If so, I wonder how this fee could be amended for people who never carry cash.
Probably a flat minimum. In the US I'd imagine it'd best be a log curve starting with a minimum of "minimum wage (of an hour)" and then shifting to a % of the cash inside. Something like a gentle decay curve where every base 10 increase there's a halving of the percent cut.
$20-50 seems like a fine reward for the average person. I’d probably give whatever money was in the wallet to them.
Btw, in both countries there's a rule (at least in Poland it's in the civic law, probably more like a custom in Switzerland), that the person who found your wallet can receive some share (finder's fee) of money, in Poland currently 10%.