It could have been easily done with a large crawler crane mounted on a large barge, and using a "spreader bar" with multiple slings.
I feel the Indonesians are seriously lacking in technical skills and knowledge in this area, or they have simply not canvassed the available options - by way of people with appropriate knowledge, and by way of local companies who possess such equipment - for effective recovery of the likes of the fuselage and wings.
The attempts to drag aircraft components bodily from the water using winches, a la fishing nets, is doing nothing to promote their desired image of competence in recovery techniques.
Indonesia has plenty of capacity in this area. It has a sizeable offshore oil and gas industry and salvage operators would not be ignorant to salvage techniques. It's much more likely to be an issue of access to resources. Do people think the kind of specialised resources suitable to this type of offshore salvage are just waiting around in close proximity on call to respond to this kind of event? it can take weeks to mobilise specialist resources,which more than likely will already be tied up in current and planned commercial operations.
There has to be a weighing up of costs and benefits and availability of resources. And maintaining current morphology is not actually essential for incident investigation.
Most of you are living in some kind of fantasy land. Sad, traumatic and important as this is, it's not something the world stops for.