The thing with a feint is that it doesn't necessarily mean you're even going to kick them; usually the opposite so you feint a kick then elbow or punch them (which is serious if you've just rushed into range).
What I'm slowly beginning to realise is that it is no sense dealing with 'a kick' or 'a punch' or 'a grab' they are all generally far too fast for you to snatch out the air. What we're really doing is dealing with their body;
punches reveal vital areas and allow you to unblance them, kicks are even easier. Whether you take someone down from a feint depends whether they have actually displaced their body (hips or balance/centre of gravity) to initiate this.
N.B. if they don't commit a punch it is hard to unbalance them because they are pretty stable and you have to force them over (or hope they just like leaving their arm out for an application). I think atemis/strikes/more aggressive entering are the best ways to deal with this and hope they don't do aikido! If they don't give you any yin you can't reply with yang.
I don't see any easy answers.