If you are fine with QFN, then BGA shouldn't be a problem. IMHO, QFN is actually a more difficult version of BGA, since the balls give a tiny bit of extra flexibility against the amount of solder. Like, if you push it down "too hard" during placement, the paste does not squeeze out and short pads like it does on a QFN package, so self-alignment during reflow has higher chances of working instead of the whole thing getting stuck at offset.
Having larger number of pins isn't the problem. If you are having any sort of yield problem, that will show even with just on a 16-pin QFN.
Yeah, you can't visually inspect. For production you want X-ray (for cheap product, random samples, for higher end stuff, every unit). In lab use / prototype, you just do functional test. Most difficult situation is if you have to manufacture small batches (tens of units) for customers quickly, and don't have an X-ray. Even if you do functional test, how do you know the units work after shipped, or in higher vibration environment? Some of the joints could be marginal and pass the initial test.
Of course if possible you want to avoid the smallest pitches. On the other hand, I hand-soldered dozens and dozens of tiny BGA 0.5mm pitch image sensors, and I'm not stellar at this kind of stuff. I didn't even have much visual clues on the correct placement, but over 95% of the boards ended up working just fine, which required basically all of the pins to function (parallel bus, many voltage supplies, etc.)