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.
The British use pound for weight and pound for currency, the Chinese use the word yuan for currency and many other things, without confusion.