The only reasonable APS-C advantage is the price.
If we stop right there, I agree. You also stated, "
If 5D3 had 46mp sensor, then you could crop 18mp image out of 46mp and it would be just as good as your 7D image and much better when you don't need to crop it," which is tehnically correct, but practically irrelevant since the 5DIII does not have 46 MP, nor does any currently available FF dSLR. By your logic, if the
Canon 5200mm lens was the size of an 400/5.6 lens and could be mounted on a Phase One IQ180, and that Phase One could shoot 10 fps at ISO 25600, I'd have the perfect birding setup. See how 'if' is pretty unhelpful, sometimes?

Indeed. I use a 7D and a 300 2.8, sometimes with TC 2x.
Wanna know what FF equivalent is? Roughly the 500 f4, a heavier, slower, more expensive lens.
With TC 2x on my 300 2.8, it becomes a quite usable 600 5.6. The ff equivalent? The unwieldy, beastly, expensive 800 5.6, and that's still not there yet. And with wildlife, birds especially, a frame filling image will require you to stop down to f8-11 often. The advantages of ff are there, but they are rather mitigated by reality.
Quite useable, I agree. But not 'the same' or even 'nearly as good'. I'm not going to compare my 7D + 100-400mm (640mm FF equivalent) to my 1D X + 600mm f/4L IS II - that's vastly unfair given the two lenses in question. But to take something close to your example, compare two superteles - a 7D + 200mm f/2L IS (320mm FF equivalent) with a 1DsIII + 300mm f/2.8L IS II (
link). The FF + 300 combo is noticeably sharper. That's true even if you go back to the older original 300/2.8L IS (
link).
I like my 7D - a lot. But a FF camera delivers better IQ, period. If it takes a longer lens to get the reach you need with a FF body, and you use that longer lens, your IQ will be noticeably better. Maybe the 7D with the shorter lens delivers IQ that's good enough to meet your needs. Maybe the 7D with the shorter lens is the limit of your budget. That's reality - and it's mitigated only by your budget and ability to carry the lens(es) in question.
Let's face it - Art Morris
could just use a 7D with his 800mm f/5.6L IS, and have 1280mm, but he doesn't - there's a reason he is so thrilled that he can get a 1D X to AF at f/8 with the Kenko 1.4x on the 800/5.6 and get to 1120mm on FF - it delivers much better IQ than a 7D.