Under the new and much unimproved FS, when a record is identified in search, there is no option to indicate not a match. When a possible record is identified under similar records, there is no way to indicate not a match.
I do not understand why you believe that all records found in a Search or as Similar record should have the ability to mark them as "not a match". These search options cast a "wide net" in attempting to locate records that might be related to the individual being investigated. It is assumed that there will be many records that do not exactly match the individual and your job would be to evaluate and determine if any of them really are for the person being investigated. If they were marked "not a match" all it could do is prevent them appearing when another search is completed. I do not see any advantage is doing that and it adds significant complexity to the search routines. For each person in the tree there would need to be a list of not-a match records. I would suggest that the benefits are not justified with the effort required.
Fair question, justification of effort required depends on one's perspective. The programming effort to allow users to mark records as not a match is not insignificant, as you described. Since this effort does exist for record hints, the complexity effort seems to have been at least solved.
However, the effort on part of many users who see the record with no indication that another user has marked it as not a match also is not insignificant. At the least it warns someone to be extra careful to examine the record and at best allows someone not to spend any more time on researching that record, unless one really wants to do so. Whether from search or under "similar historical records," unattached records are presented to everyone who accesses those screens. Each time they must be investigated again. To allow them to be marked not a match, with an explanation, would save considerable time and effort across the user universe.