I think that while there is plenty of reasoning behind going to trail runners, I have always been completely against doing it. No, it has nothing to do with ankle support. It is healthier for you to hike with your own natural ankle support and build the proper muscle and technique. However, a lot of hiking happens in places where trails are narrow, have protruding rocks and roots, and I find that while I don't need the ankle support, I want the ankle protection. Hitting your ankle on things is painful. I spent a while trying on different boots, hiking with different setups, and I went from a stiff leather backpacking boot, to a running shoe, to these:
Solomon XA Pro 3D Mid Ultra GTX® Boot.
I found these boots to be liberating. They are very light compared to other boots, you get the added protection of goretex, and they feel like you are barely wearing anything on your feet. There are plenty of other boots in this category - light, good flex, ankle protection, and not much heavier than the average sneaker. I am a convert to these new lighter weight boots. There is also another great option from Adidas:
Adidas Terrex Boots
These are newer design, also light, waterproof, and flexible.
I much prefer to keep water out of my boots and keep my feet dry with a mid boot and a gaiter, then to suffer with uncomfortable wet feet. Because yes, you can keep them warm, but who the heck really wants to hike all day with damp feet sloshing around? Good way to get athlete's foot, or to just weaken the skin in general by abusing it - I still don't get why anybody would be ok hiking in these conditions, or why they would prefer to use a shoe that wets through with the introduction of even the smallest amount of water. To me that is a danger on longer trips. If your feet are damp and getting hard use, they are at risk, and I never want to be at risk in the backcountry.