Spending thousands of bits on small things will remind people of currencies that have been hyperinflated.
Besides, we already send plenty of bits and kbits over the internet; it would be confusing to try to reappropriate such a word.
In what way? What is an example of how bitcoin bits could be confused with informational bits?
A data plan priced in bits, like "Unlimited downloads for only 2k bits per kbit", could be pretty confusing. 2kbit / kbit? Huh? Though I like the idea. I just think a nice easy term for a millionth of a bitcoin would be good. And a bitcent could be reappropriated to be the same as a satoshi now, aka 0.01 bits. That way, like with most currencies you use every day, you would only have to deal with at most 2 figures after the decimal place. Unless the protocol is changed in the future to divide bitcoins up even more.