Lots of answers to questions OP didn't ask.
OP, with few exceptions, if live sports is important to you, you need cable or SATT unless you can get the live sports you want over-the-air (with an antenna) or you want to go the pirate route.
With few exceptions, if seeing TV shows when they first air is important to you, you need cable or SATT unless the TV shows you care about can be had over-the-air or you want to go the pirate route.
So much of the "cord cutting" mentality revolves around sticking it to the "greedy" Cable company, though the Cable company is going to get theirs through the broadband fee anyway. The solutions often involve tradeoffs that may matter to some people. For example, some "solutions" trade off quality of picture or make you wait hours or days or seasons to get to see new shows. The app alternative tends to trade off on-screen guides which brings all available programming together at a glance instead of making one hop app-to-app to see "what's on now?" or requires someone to know what they want to watch and where they are likely to be able to find that show. DVR "solutions" tend to be less than SATT or cable DVRs in that they can't readily connect to every video stream available to you- just those compatible with whatever DVR alternative you try to make go. Some cord-cutter solutions require hopping box to box to be able to find what you want to watch because there is no "one box to rule them all" (like a SATT or cable box). And so on. Some don't care about such tradeoffs but others do. In general, it seems to work best for the tech savvy who doesn't mind jumping through the hoops to get to what they want. Those with families that aren't all tech savvy will feel pressure to just pay the money to make it easier for that family to watch what they want to watch in a simple, "just works" way.
As to the monetary motivation, I suggest looking at DISH's 3 year "price lock" for $49/month offer
http://www.dishpromotions.com/dish-network/get-dish/dish-network-3-year-price-lock-offer/ which seems to be about the best option available for live sports and live shows without it running to more traditional cable price ranges. Pair that with an over-the-air antenna for highest quality locals. And their offer throws in one year of Netflix for free. Good HD quality. A unifying, all-possible-programming DVR. No waiting to see first run shows. Etc.
Every one of these threads crack me up. Here's a bunch of people frothing to buy anything and everything Apple dishes out and pay up the so-called "Apple Premium" (and easily justify anything & everything about every such purchase) but we can't seem to see much value in the SATT or cable TV package proposition (that is, until Apple rolls out some kind of TV channel/programming package via subscription and then we'll have no problem rationalizing that one). I just spent more than the cost of the typical SATT or cable MONTH to take the fam to see Batman v. Superman for about 2 hours but I'm apparently supposed to be appalled at getting about 108,000 hours of programming (200 channels with about 18 hours of programming times about 30 days) for less??? What a ripoff!!!

Now let me go wait in line to buy one $8 cup of coffee.
OP, isolating the part of your question about "is AppleTV good enough", I'd offer this (with apparently very similar programming preferences as you): AppleTV is an excellent
augment to a good cable or SATT subscription package but not a replacement if one wants live sports and first run programming when it first runs UNLESS you can get those 2 wants fed by the more limited options that comes with "cord cutting". In short, if you can scratch both itches with the big 4 or 5 networks and live somewhere with good over-the-air reception of those networks, you might indeed be able to dump cable or SATT and go with an over-the-air solution + AppleTV. But as soon as some favored sports or show(s) are
only available on a selection of cable channels, the workarounds are poor to nonexistent.
Beyond television, AppleTV is also fantastic for so many
other things (music jukebox, photo albums on demand, home movies on demand, vodcasts, podcasts, video on demand, airplay, etc). If you are trying to rationalize buying one, you don't necessarily need to do so solely revolving around replacing a cable or SATT subscription with one. Instead, any/many of these other benefits might be enough to justify the relatively cheap expense of this little box.