Actually, collecting is the first and arguably most important step, and one that's continually ongoing. Thomas MacEntee is credited with developing "The Sevens Cs" for genealogical investigation, and for the studies I've undertaken I modified those slightly into "The Seven Cs of One-Name Studies": Collect; Curate; Calculate; Create; Connect; Conserve; Continue.
I believe something fundamental in this Question is a possible misunderstanding: one-name studies can include genealogy and pedigrees (you probably won't find any of the Guild's 2,254 registered studies on WikiTree that don't include pedigrees), but that's only a portion of what one-name studies are about. Here's an example, as an image file, of a Venn diagram I did for the Threlkeld ONS. Family histories, pedigrees, and artifacts (like unique documents, photographs, audio recordings, etc.) comprise only one of five elements of the study.
The foundation of ONS really began with the Guild of One-Name Studies and its start in 1979. Here's a good, but brief, introduction to what one-name studies are: https://one-name.org/one-name-studies/.
The Cliff Notes version is that one-name studies are not equivalent to genealogy. They really have nothing to do, explicitly, with WikiTree profile improvement or individual biographies, and aren't even solely focused on pedigrees or descendancy.
I first joined WikiTree because of my Threlkeld ONS. It offered a free toolset and collaborative environment for the pedigree and genealogy portion of the study, something for which I'd previously been using an application called WebTrees. For an ONS, this is a notoriously difficult aspect to manage for collaboration (understandably so, since most volunteers are generally interested in their own family), and WikiTree, for me, offered the best solution. It was several years later that WikiTree implemented its own version of one-name studies and, happily, it was designed with a great deal of flexibility for the administrator to define how a study would be structured and where its efforts would be focused.
I agree with many that utilizing the sticker on profiles for one-name studies can be intrusive and should probably be restricted only to those profiles of some particular interest. I admit that some profiles in my studies still bear stickers because, in the early days of WT ONS, that was the standard practice. But since the Categories were moved a few years ago to the bottom of profiles, I can see no reason that name-study categorization should be an issue.
That said, I'll also note that there are differences of opinion about whether or not individuals collaterally associated with the surname (e.g., by marriage or adoption) should be considered part of the actual ONS. In my case, I opt not to include them; only those born with the surname or known variants.