My telly has an ethernet port
"Why does an HDTV need busybox at all?"
The manufacturer of just about any electronics that talks TCP/IP has the choice between:
a. developing software from scratch.
b. paying for a license to use a proprietary software stack.
c. using readily available open source.
Obviously c. is generally the most cost effective option, but if the variety of open source license is copyleft, then it comes with a legal obligation to make available source code including any modifications made to it to those to whom the software embedded in the hardware is distributed.
It's true that cheap display devices don't need to talk TCP/IP, but more expensive ones do nowadays and people paying money for HD generally want their tellies to be able to select and display from a variety of media, including media deliverable over a home network.