The issue here is not whether this is a good idea, but rather whether it is feasible or practical to implement.
The browser extension that Jim mentioned enables us to put Other Last Names on the initial Add Person form (the feature that you asked for). It does not insert them into the matching process that is done when we start to create a new profile (the feature that you actually wanted to have).
The matching process for Add Person is designed for fairly simple cases of duplication. It's not intended for the kind of research that's needed for complicated situations like what you describe. And we have members who complain (appropriately so) that they are overwhelmed by the number of matches they are shown, particularly when there are many similar names. Fortunately, Name Search allows us to (1) query all name fields on existing profiles (2) sort and filter our results (something the Add Person form does not enable). This allows us to focus on the most relevant results. (Yes, we may need to search on the multiple names a person might have used, but it's more efficient to do that in Name Search than on the Add Person form.) When I run Name Search before creating a profile, by the time I get the list of matches on the Add Person form, I am rather sure the person doesn't already have a profile, so I can review the match list (even a long list) very quickly.
Jamie and the Tech team are working on additional improvements to Search functions here, but there are many challenges (some of them related to technical things like computer memory) to be dealt with.