Your MAC will only be known to the router of the coffee shop and the router's MAC will only be know to their ISP's router/modem. The ISP MAC will be in the logs of all the servers you and other cafe customers access.
I don't think this is correct. The servers you connect will see an IP address only. This could only be converted into a MAC if the IP was resolvable locally via ARP (i.e., you're on the same LAN).
The danger of retaining your real MAC should be obvious; it's a unique identifier specific to your machine that will at least significantly narrow the scope of the machine/owner your adversaries are looking for if it doesn't give the investigators a direct link back to you (e.g., manufacturer records MAC addresses next to serial numbers, adversary gains access to manufacturer's data and sees "MAC X / Serial No Y sold to consumer Z online").
Depending on the configuration of the router on the open access points, it may be possible to retrieve a list of all connected MACs over the whole lifetime of the router. Then they simply have to correlate, "OK, which machines had a lease when the access from this machine was made?", and then investigate the 5 matches that come up.
