More foot patrol is always possible. Back in the days, all patrol was foot patrol. Our almost complete dedication to cars responding to dispatched calls is a choice we make... or maybe a choice made for us. But if we really wanted and demanded more foot patrol, we could have it. Police departments need to defend car patrol with something better than tradition and response time. Here's an op-ed I wrote a few years back for the cause.
One of my favorite pictures shows how it was done in 1911 New York City, at least in theory. Maybe today cops shouldn't stand in the middle of intersections like bowling pins, but the idea is better than any patrol done today.
(If anybody knows the source of this picture, let me know. I got it from an old Yale Alumni Magazine. They could only tell me they thought it was public domain.)