Leia springing Han and getting away doesn't solve the problem that Chewie and the droids are also still prisoners/possessions of Jabba. Maybe the assumption is that Lando could then get them out without getting Luke involved/captured but with Jabba still alive he'd be furious and could lead to who knows how many more issues. We also have Boba Fett to contend with going forward.
Long story short: If you change the timeline as suggested you may radically alter everything else and it doesn't lead directly to the path you laid out where Vader/Anakin survives.
Much easier it is to just let Yoda hang on a little long to teach Luke a bit more. Also possible that Vader simply survives the "final encounter" with the Emperor although there would be questions of his condition at the end. Assuming things go as they do in the movie except Anakin survives the last encounter there are multiple ways things could go.
The easiest way to end the war/rebellion could be to have Vader assume the mantle of Emperor and declare an order to stop and offer the reasons why. This assumes that Vader would be accepted as the new Emperor far more easily than any of the others who wanted to take his place along with an idea that Vader may have had better knowledge/understanding of all of the Emperor's other dealing. Now would Anakin be in position to do this as a prisoner of the Rebellion? Unlikely. I'm also not sure that a "public display" of capturing Vader instead of him falling would do them any good.
Now if Vader still dies at Endor but Luke somehow manages to rescue the old war hero Anakin Skywalker it may not immediately change things although it could actually be a boost to resistance morale granted Leia knowing the truth may have a harder time accepting all of it. Here the question simply may be how long the Vader is Anakin secret could be kept because Anakin certainly could provide a wealth of knowledge about the Force as well as the Empire and other things.
Looking out way in the future Anakin's survival may completely change the Destiny of one Ben Solo if that is the timeline you choose to follow.