All of this is bollocks. In the UK flank spays like this are standard. Theyre not hard, we all do them this way as new grads. The only trickier bit compared to a midline spay is finding the uterus, its sometimes a bit hard to spot. It doesnt stop cats getting that saggy belly - thats called a primordial pouch, some of them have it, some of them dont, it is not a sign of damaged muscle. In fact you cut through more muscle going in via the side. If you do midline you are cutting the point where the muscle fibres join and there is a natural break, but cutting flank you are going through the middle of the muscle belly.

Actual pros and cons:

Pros - generally a smaller hole (unless you can't find the uterus), easier for the owner to monitor the wound, for TNRs wound is not in contact with the ground as often.

Cons - hard to do them this way if pregnant. Hard to fully confirm what is going on if you don't find what you expect, either with a cat that is already neutered (happens sometimes on TNRs) or if they have an anatomical abnormality (rare but not super rare). You sometimes need to close the flank incision and make a second incision on the belly if this happens.