That actually convolutes the points. Memorization isn't due to cursive, but overall brain development is.
Learning cursive can accelerate overall brain development. Both the reading comprehension types of tasks and the motor skills tasks cause an overall cognitive increase. And a lot of this data is pretty spurious. You notice these are all news articles, and many of them are full of fluffy anecdotal info -- none are psychological studies. The data saying things like "SAT takers who write essays in cursive score higher" aren't particularly well studies. Correlation is not causation, and it could be that those same students might be more comfortable writing, or are more likely to come from a home where writing is valued, or that schools that still teach cursive might also be generally more academically focused, or a dozen other things.
Mostly, you know it's good to learn, and you know it isn't bad to learn, but a lot of the benefits of learning a new writing style are more likely to show up in younger children, where the plasticity of the brain is significantly greater than in an adult.
As far as remembering content, like from a specific lecture where you take notes, it doesn't matter what hand you're using. You remember much better with hand taken notes. This goes right back to the foundations of how we learn, and how we process short term memory, which is very limited. Most people can only remember about 7 items in short term, any more come in and they'll lose some items from that list. They have to process that information into long term memory if they are to retain it, and that processing is where the hand encoding helps.
In my fundamentals of instruction books they said there were three learning methods -- Visual, Auditory, and Tactile. If you can combine more than one, you will remember better than just one. If you use all three you will often learn more quickly, still. Hand writing is tactile AND visual, and has a sort of special extra something as your brain has to process and encode the data so far more of it makes it from short term to long term memory. Typing isn't the same as it doesn't require the same type of mental gymnastics, and reading someone else's notes or a handout sheet doesn't engage the tactile sense at all. That's why people learning a new alphabet gain recognition more quickly when they hand write the characters -- the process of visualizing then recreating the character forces your brain to process it and then reinforce itself tactually and visually.
Additionally, taking lecture notes by hand forces a student to make choices in what is written down, so it actually tends to increase concentration on the lecture. They focus on key items and only get the tactile and visual learning center engaged on those items so, as a result, they create memory triggers that help the brain to recall more extensive information. Very much like mnemonic memory techniques, the brain often stores a LOT of information that you just can't access unless you have some sort of trigger that starts the recall, and good note takers end up reinforcing enough triggers that they can recall a lot of what was not written down when reviewing the notes.
That was the explanation I've been looking for. Thank you for that. It was very interesting.