All the modes have their place.
If you're shooting moving things in consistent lighting but inconsistent backgrounds than manual works great (on moving or static things!)
Lets say I'm shooting eagles on a cloudless day, for example. They can fly with the sky behind them or with the dark trees behind them. I set it to AV and take a few test pictures of something of neutral color (like green grass) and then make sure the exposure is right via the histogram. If it is, I look at the settings and switch to manual and use those settings.
Since the lighting won't change (either by cloud or because the eagle is in the shade), the exposure will always be right.
NHL puts forward that if you set it to Tv you can go for a specific look (slight blur in the wings) which I will only get by luck.
If I'm shooting warblers or other small birds that go between shade and sunny spots then I shoot in Av. This lets me get the max shutter speed all the time while always controlling the depth of field and always getting the proper exposure. I do need to use exposure compensation when the background changes radically, though. And I do miss some shots because the shutter speed goes too low... so it goes. The odds are that the recovered image (lightened in PS) won't be of good enough quality to make me happy any ways.