I'm not opposed to the carts, though I will say as a general rule I do not patronize street vendors, particularly when it comes to food. I felt the need to speak out because I felt that some of the posts in this thread were attacking newer residents of the historic district unfairly by siting them as the root cause for Ms. Sears' position on this issue. You seem to agree with that viewpoint, which is your prerogative.
As for the second part of your reply, you are undoubtedly biased if you don't think the sidewalks on Roosevelt Avenue are too crowded and filthy to easily navigate as a pedestrian. And no, this is not just because of the food vendors, but their presence does compound the problem. The carts in front of the subway station/bus terminal always create an obstacle, particularly during the evening rush hours. There is often some liquid on the sidewalks by the food vendors, whether it is melted ice, discarded washwater, or spilled beverages and condiments. (I'll add that I don't particularly care for the noise or smell that emanates from the portable generators some of the carts use either.) And it's hard to deny that they don't bare any responsibility for the litter problem when you examine what's often found lying on the streets.
That being said, I do not support a "draconian" solution but neither do I think it's unreasonable to require the vendors to relocate their carts during busier times of the day. This is what is often done in Manhattan... Vendors must move from the avenues to the side streets at particular hours.