Agreed on this generally, except that I know some people are just really set on starting next year. If you just really want/need to get into grad school, nothing wrong with applying to some schools you might not have otherwise considered. I ended up loving my initial least favorite schools and hating my initial tops. You get a different view after interviews. One of my "safeties" ended up being the main contender to the program I ended up choosing because at interviews I learned that they had some of the biggest names in a specialized subfield I was interested in, even though they didn't generally have as good a reputation as some other schools I got into.
Moral of the story: focus on schools with faculty doing stuff you're interested in, not well known schools. Don't Google schools and check their faculty lists, Google people and check where they are. Ultimately the research you do is most important (not that institutions reputations don't matter, but if you can be successful in a lab matters more).
I think you're aiming high, and at the very least need to diversify your list to include some schools where you can be more confident that you have a shot at admission. I would recommend applying to at least 5 schools. Without knowing the area you're interested in doing research it's hard to make recommendations, but I'm sure if you add more schools you're interested in to your list, then people here can give you more feedback.