This Site would have all wallets like the digger on the exact date to do the digging, otherwise to promote the coin they just go to an exchange and buy these clam.
If you find wallets with balances just on that exact date it would be evidence of cheating.
More likely that the balances are there before during and after the cutoff date. That wouldn't be all that unusual for any site that keeps balances on many addresses (for example, gives each user a different deposit/payment address and doesn't automatically sweep everything right away).
As for going to an exchange, that has a liquidity cost. Right now to just buy 20k CLAMs you would double the price and many of those CLAMs would be bought well above the market. You then risk being unable to liquidate except at substantially lower prices. That might very well discourage new participants in a way that being able to claim a bunch of CLAMs would not.
as far as i know, no one wants to remove the digging feature, just slow the digger down..
Some have certainly suggested eliminating digging altogether, or imposing a tax that would make it worth a lot less going forward. I don't really see a good method to just slow it down, and especially not slowing down larger diggers without making it prohibitive for smaller ones.