Do Embedded Internet Systems make sense? I believe the answer to this question is yes.
Why? Embedded systems are often "embedded" within equipment. The location of the equipment could be on a remote mountain top, located in a class 10 clean-room, or in many other difficult to access locations. The location could make internet remote access attractive and very cost-effective. A decision to use internet protocols to access the embedded system provides a rich set of standards, and tools (including browsers) which may result in a reduction in the cost of engineering the embedded system.
Are there any problems in implementation? Could be. Internet protocols could compromise the real-time requirements of some systems. In a system with enough resources, and with a true real-time kernel, there may be little, if any problem servicing the network interface as well as the embedded application itself.
Read here about an evaluation project using the NetBurner product.