Is it beneficial to replace the top on a cheap but sturdy fiddle?
No. Tops aren’t interchangeable, and the cost to have one made will be considerably more than that of a new one.
Theoretically, if you had two instruments from the same maker and of the same model and size, the tops could be exchanged. However, even largely machine-made violins are still not quite that consistent, and the cheaper the violin, the lower the chance of anything being consistent.
I actually have a couple of composite violins in my shop, and have seen others, and you see stacks of parts at "trade" auctions, but all in all, the operative word here is "cheap". You can buy a pretty good cheap fiddle for what you can change tops for, if you are paying for shop labor.
One exception - I'm told you can buy replacement tops and necks for Kay basses, and they are pretty economical.
Yes, there are composite violins. It does sometimes happen that a top will fit into another instrument, but it’s not common. In some cases the top is altered to fit onto the rib structure, but that requires a lot of skill to work well. So I wouldn’t say tops can never be exchanged, just that the odds are not favorable.
'Fiddle Lesson - Jenny Lynn' 13 hrs
'Chin rest' 3 days
'The Nightingale' 4 days
'The Nightingale.' 4 days