Semi-enclosed spinning reels really work well for my kids and these are interesting models to me. They have some semi-enclosed abu and daiwa reels that they like that have push buttons on the face of the spool. They prefer these type of reels to trigger activated underspin reels because they say they get better casting with ultralight lures and I agree with their assessment. The larger opening seems to cast better and I would assume that is because there isn't any bend in the line going to the center hole like the closed face underspin reels. At any rate, I am proud to have two young kids that enjoy fishing enough to take the time to notice the differences in reels! They fish out of their own kayaks along side my wife and I on small rivers and creeks and they aren't comfortable with regular spinning reels yet and still get tangles. The semi-closed face spinning reels give similar castability with less fuss/more time actually fishing.
Maybe someone knows of other similar models that I haven't discovered?
This is a niche market for sure but I am a little surprised these type of reels aren't still being produced by more companies. I think Abu and Daiwa (Abu 704 and Daiwa 125M) still make some that are pretty pricey and geared toward match/coarse fishing in the UK. Not many options here in the United States.
Here are some pictures (I found online) of the Shakespeare models for reference:

Thanks in advance for any info and or other models made in a similar manner some of you might know of!