This is a known bug, or a known missing feature depending on how you look at it.
The short summary is that Dolphin doesn't regenerate the H3 hashes and doesn't fakesign the disc. Dolphin with its IOS HLE ignores incorrect hashes and signing when you try to run a game, but a real Wii does care, and so the files that are generated by Dolphin don't work on real hardware. The incorrect H3 hashes generate a medium severity warning in Properties > Verify, by the way.
So why doesn't Dolphin support doing this? Well, the way that a normal converting program would most likely do it is: First you write out almost all of the disc, calculating the H3 hash for each part of the disc as you go. Then you seek back to the area close to the beginning of each partition where the H3 hashes are, and write the H3 hashes. Then you perform fakesigning, and write the fakesigned TMD just next to the H3 hashes.
Those steps have to be done in that exact order in order for all the necessary data to be available. Now, what you have to keep in mind is that Dolphin's support for extracted disc images was originally designed only for the purpose of running them, not for converting them back to a normal ISO. (The ability to convert them just kind of ended up being possible as a side effect of how Dolphin's disc formats code is constructed.) Implementing H3 hashing and fakesigning for when you run an extracted game would be rather awkward, since if you ever want to read the TMD or the H3 hashes, Dolphin would have to read through almost the entire game, which could cause it to have to pause for something like a minute. Technically it could be implemented in that way, and then converting would give you the result you're expecting, but then the conversion process would have to end up reading the whole game twice (first for calculating the H3 hashes and then for real), with the progress bar just being frozen the first time. Implementing a special solution just for converting (along the lines of steps I described earlier) wouldn't be impossible, but the way Dolphin's disc formats code is structured right now would make it rather ugly to implement. After all, Dolphin is primarily aimed at letting you play games, not at letting you convert them. And so this is a rather deprioritized feature.
The short summary is that Dolphin doesn't regenerate the H3 hashes and doesn't fakesign the disc. Dolphin with its IOS HLE ignores incorrect hashes and signing when you try to run a game, but a real Wii does care, and so the files that are generated by Dolphin don't work on real hardware. The incorrect H3 hashes generate a medium severity warning in Properties > Verify, by the way.
So why doesn't Dolphin support doing this? Well, the way that a normal converting program would most likely do it is: First you write out almost all of the disc, calculating the H3 hash for each part of the disc as you go. Then you seek back to the area close to the beginning of each partition where the H3 hashes are, and write the H3 hashes. Then you perform fakesigning, and write the fakesigned TMD just next to the H3 hashes.
Those steps have to be done in that exact order in order for all the necessary data to be available. Now, what you have to keep in mind is that Dolphin's support for extracted disc images was originally designed only for the purpose of running them, not for converting them back to a normal ISO. (The ability to convert them just kind of ended up being possible as a side effect of how Dolphin's disc formats code is constructed.) Implementing H3 hashing and fakesigning for when you run an extracted game would be rather awkward, since if you ever want to read the TMD or the H3 hashes, Dolphin would have to read through almost the entire game, which could cause it to have to pause for something like a minute. Technically it could be implemented in that way, and then converting would give you the result you're expecting, but then the conversion process would have to end up reading the whole game twice (first for calculating the H3 hashes and then for real), with the progress bar just being frozen the first time. Implementing a special solution just for converting (along the lines of steps I described earlier) wouldn't be impossible, but the way Dolphin's disc formats code is structured right now would make it rather ugly to implement. After all, Dolphin is primarily aimed at letting you play games, not at letting you convert them. And so this is a rather deprioritized feature.