The real problem is making inking work with any arbitrary control! That is what the current input panel is for. Remember it has to work anyplace anyone could ever enter text, wherever a cursor appears. So that includes Bob's Janky Control Factory DLL version 1.32a last updated on October 3rd of 2008.
If you search MSDN, there are plenty of examples of some really awesome ink enabled controls! Designing a system for ink first would be a lot of fun! I remember controls published for web pages that supporting inking, forums you could just draw right into the reply box on. Really cool stuff.
There is also usability concerns, not everyone has hand writing small enough to fit inside of a single line input box! Increasing the area to outside the box only works until the tip has been picked up, if you make the user always start the inking inside the box maybe something could be worked out, but that'd be a very unnatural way of writing.
Perhaps Metro apps were an opportunity to change the behavior and shed legacy compatibility requirements. Another possibility is to target just the web browser; the web has a defined set of controls which allowed Apple to define touch behavior for just those. I agree tackling compatibility for everything that has ever been created in Windows is not feasible, but I think there are alternatives.
Regarding size of input box, remember how small people write on typical ruled paper. It's much smaller than the handwriting recognition area! The reason I thought just letting people wander outside the box might work is that most of the time, it's for letters like 'g' or 'j' where part of the letter hangs 'below the line'. Characters don't typically start below the line.
In general, yes, there are many potential usability concerns. However, the bar is low, as most people don't consider the current system usable to start with.
As the OP points out, the pop-over handwriting "keyboard" is far from ideal. So far, in fact, that I feel it neuters the appeal of the pen on my Surface Pro. I don't want to lose half my screen real-estate to a special-purpose input area, be it a virtual keyboard or a special handwriting panel. Losing half the screen for input reeks of the iPad.
I have one small suggestion, if you don't mind: How about making the input box increase in size (maybe double in size) so you don't have to write so small? The resizing wouldn't need to reflow the rest of the page; it could turn into a modal textbox in the same location as the original textbox. It would make it easier for children, the elderly and people who aren't native speakers of the language, etc.
And of course, there is still the option of scaling the page overall. It's possible the audiences that would want bigger input boxes would also want the text and images to be bigger as well, but it needs research to confirm.