When you get towards ADSL speeds, the limiting factor in download speed could be the server, or a network link between you and the server. With modems, it's usually the modem. ADSL could well have those error checking bits, and we might never notice.
What Circus said about doing error checking at the TCP layer is a good point too. The reliability of ADSL might be such that you don't need to check every single byte that goes thu, just checking each packet might be enough. When you get into fibre, the error rate is so low as to be almost irrelevent (0.00001 or lower) so you'd be silly to check each byte.