In reply to:
Some wireless access points act as DHCP servers (my old Netgear WG602 does)
Are you certain? There have been a number of variants of the WG602, but I've never seen one that provides a DHCP service.
A DHCP service alone wouldn't help anyway, as the cable broadband network wouldn't know anything about the IP addresses allocated by DHCP. You would need address translation (NAT) as well, effectively making the wireless access point into a router rather than a simple access point.