To be clear, component as a transmission means, can readily transfer 1080p. Its close cousin, VGA does that all day long in computers and Xbox 360. Reason you don't get 1080p output from component in Consumer Electronics gear is due to an unwritten rule to help shift the consumers to HDMI and its protection means (HDCP). So it is a choice they have taken, and not based on technical or licensing restrictions.
That said, since BD content is usually film based, it is by definition progressive. So even though you are sending 1080i over component, any half competent display or processor will convert it back to progressive just the same. So the fact that you can't set it to 1080p should not be a big loss.
Alas, there can be issues. Namely, since component is not an often used standard, companies have cheapened out its implementation. Some displays will not resolve the full 1920 horizontal resolution over component. You can test for this by using a test signal such as exists on DVE. Of course, if the display is older and can't resolve 1080p anyway, this is a moot point.