You can only check them with an x-ray machine. The only way to rework them is with hot air. They suck, suck, suck for (DFM), design for manufacturing. Always try to design with leaded parts if you can. They can be fixed with a soldering iron.
Board space isn't the only consideration, by far. You don't need .4mm pitch BGAs on a giant pcb with acres of empty space either.
PCBs are not built at the north pole by little magic elves.
BGAs and LGAs are the devil, sure. But anyone who can't handle QFNs and DFNs has no business calling themselves a modern electronics shop.
(Regular QFNs, I mean. Dual-row QFNs are sick jokes, and I maintain that triple-row QFNs are just figments of my nightmares, and I won't listen to anyone who says otherwise.)
I will give you this anecdote: I find BGA easier to solder than QF[N|P]. Most soldering errors I make are due to inappropriate amount or uneven solder application. No factor if the solder is pre-applied.
In production manufacturing solder paste is generally applied to BGA pads. The amount of solder in the balls is less than the ideal amount for making a good joint, and the solder paste also helps to hold the component in position.
That said, I have ‘successfully’ soldered small BGA components by just applying a sticky flux and then reflowing with a hot air gun. It can work fine for prototypes, but it’s not really how the packages are meant to be soldered.
Unfortunately cheap accelerometers are invariably leadless.
I don't know why such a common part still can't be assembled reliably on the usual cheap one click services... But I spent several days chasing that error, thinking it must have been my design....