A lot of users (myself included) will periodically refer OP's to written tips or useful links in our signatures to help with questions asked. You're going to make an extra step for us, which will slow down the flow of information - particularly if we forget to re-tick the box and come back later to find a confused OP.
We already have pretty spartan signatures here which I appreciate immensely. But if the community agrees that 4 lines or less of plain text per post is too unsightly to bear then it's probably time to consider doing away with signatures entirely rather than making it a nuissance for users who do want to use them.
A fair number of people would most likely whip up a greasemonkey script to auto-tick the box anyway, and that would include link spammers. [Speaking of which, if you are frustrated with forgetting to detick the box, have you considered greasemonkey to automate that for you?]
In the end, you always have the option in the control panel to turn off the display of signatures when you view pages, if that is more to your liking. Maybe a better solution would be to have that display option, plus one more that shows only the first instance of a user's signature in a given thread? I would like that idea much more. That way information is in the page somewhere, if needed, and people don't have to hunt down and re/detick anything each time they post.