As the original post suggested:
Patch: If a simple fix will work with little downside then "Why not?" Consider, points, fuel pump, valve adjusting, No great controversy for those tasks.
Rebuild: Starter, Carb, Genny, Dizzy..you get the picture. So, what skills do you have? And how much can you spend? What is it worth to you when you know what you have and...what you can fix,.
Re-manufacture: Just so you know I hate this term. Hate it. What is the difference, Rebuild? Re-manufacture? OK so maybe that is another discussion. Any way, New or crate verses do it your self.. again match skills to the task. I don't know how or have access to do crankshaft grinding...so I get to choose a machine shop to do the work or buy a new crankshaft..I can use a micrometer so I can decide when the crankshaft is too far gone. You can see that the mix of skills is at least as big a part as as the choice to fix, repair or replace. I have watched some folks buy a truck all done and enjoy it well. Watched others do every thing that they can on that truck and enjoy it well. And some are in the middle.
Engine work is not a special case. How many of us do third member work?, Transmissions? Instrument work? Generators? Some of us will try any of it and some will say not.... So the upside? I know what I can fix and I know what I have. The down side? I am the warranty guy. Still I would recommend, do what you can, learn what you cannot, add skills as you go, and have some fun while you are at it.