I don't think they would really mind, it's not harming them much (I mean how big a business would it become), and it encourages people into the game more.
They mind. The only way you can win a copyright and/or trademark lawsuit is to show you have defended your copyrights and trademarks at all times. If they allow someone one to knowingly make tiles that use copyrighted art work, copyrighted game mechanics or trademarked items, then it could be considered dilution of copyright and trademark. Enough dilution occurs and they could lose trademarked items first and then copyrighted works second. There is too much money being made by HiG and RGG for that to be allowed to happen by their lawyers.
The United States has some of the strictest laws concerning copyright and trademarks. And the leading company that helps lobby for those laws is Walt Disney. If you want some very dry but interesting reading, check into how Disney is constantly having the laws changed to protect Mickey Mouse as a copyrighted and trademarked item.