For your car yes there is a huge downside for retrofitting an alternator, because an all original '57 is much more valuable then a resto-mod.
The good news is that both the original regulator and generator can be cleaned, checked and rebuilt. Start with the regulator. Inspect for loose wires and dirty or rusted contacts. Open up the cover and check for worn components. Buy a can of electric contact cleaner (Lowes or Home Depot) and use that to clean the interior parts.
Then test the regulator. It provides current to the generator to "excite" the electromagnets that in turn generate the electricity. Here's a video showing how that is tested.
https://www.youtube.com/watch?time_c...ature=emb_logo
The generator is more rebuild-able. Refer to the earlier video- the brushes and contacts on the generator need periodic maintenance. The bearings wear out as well. I suggest that you do the job yourself because it is a simple job. If you can't do that then look for a local electric motor rebuild shop and take it and the regulator to them.
Here a rebuild kit is less than $50, and a rebuilt generator is under $180. I'm guessing that a local shop could do it for $100.
https://www.larrystbird.com/product-...nd-alternator/
Brand new regulator for less than $50.
https://www.rockauto.com/en/moreinfo...1338083&jsn=14