You're correct, Steve, there is no problem as regards functioning nowadays... aside from the irksomeness of searching for "shanty" and getting results for other things, or the often encountered need to add the word "sea" to clarify "shanty." (By the way, I'm not being sarcastic!)

So yes, the interest in spellings presents mainly a historical/historian's "problem."

Terry, who very formally advocated for the adoption of "sh" spelling, was also the person to put forward the idea that "Maybe shanties come from people moving huts in the Caribbean." As someone interested in the historical development of the genre, I would like to be able to assess the likelihood of such a theory.

I think if Terry had all the information that "we" have now, he'd have had to dismiss his theory. But he didn't, and in fact another issues of spelling (the rejection of French) helped drive Terry towards the idea. So now Terry's idea stays there in books and people continue to consider it as the plausible explanation of an expert.

One of the key "mysteries" of chanty history is how, in Nordhoff's late 1840s account of cotton-screwers, the "chant" and "chanty-man" were pronounced - especially since "chanty" does not turn up after that until 1867 on a New York ship. Had Nordhoff used the spelling "sh", then we could be sure about the pronunciation.
Unless we want to assume that he meant "ch" as "church" and that the pronunciation changed by 1868 - an assumption that has problems with it - we must guess that Nordhoff chose "ch" to represent "shingle" sound for a good reason. The reason may have had something to do with a French influence in the environment that bore chanties (or other reasons).
Some reformers advocating for "sh" were not aware of Nordhoff's account, etc, and they assumed that later writers - not as knowledgeable as themselves about "sea stuff" - had created a fanciful spelling.
So, spelling has very much to do with both locating the "flow" of the development of chanties in the early years, and with shaping the discourse produced by those who mediated the genre (e.g. change to "sh" is a small part of making the genre appear more "English"). It has little to do with how you or I function nowadays...though a little awareness of it wouldn't *hurt* for when we read the literature on the subject.