This answer refers exclusively to "atomic" citation references based on numbers or abbreviations, such as , [ABC+95], or (M09). My opinion described here does not expand to citation reference styles that do not require a fixed form, but instead integrate naturally into a sentence, such as "Picard and Galen had discovered in 2336 ...", thereby indicating the key information of author names and year necessary to find the appropriate item in the bibliography.
As a further restriction of my claims with respect to Massimo's answer, I would like to point out that my subfield rarely uses numbered equations. If we do, they are explicitly referred to, like other inserted pieces of information, by writing "From Equation 15, we can conclude ...", rather than using the mere equation number like "From (15), we can conclude ...". This may well influence my opinion.
As a bit of a counterbalance to the existing answers, I am going to state my opinion that using a citation reference like a word is extremely bad style.
I would not point it out in a review, as it is too minor, but I definitely rewrite such sentences in papers that I participate in when one of the other authors uses that style, and I ask them to write complete sentences instead.
One issue I see with considering citation references such as  as words is that papers that do so apparently never do so consistently. More concretely, a sentence like
We analyzed the data using the Wilmerding method, guided by .
is often followed by a sentence such as
As numerous problems have been pointed out related to the basic Wilmerding method [13 - 15], we have used the Thunderbolt Approximation.
So,  is a word; it should be read as "Reference 12"? Fine, but then [13 - 15] must be read as "References 13 to 15". Evidently,
As numerous problems have been pointed out related to the basic Wilmerding method References 13 to 15, we have used the Thunderbolt Approximation.
is not a sentence.
Conversely, if citation references are considered as words, each additional reference makes the sentence more convoluted, as additional sentence parts have to be added. In particular, the action of inserting a single reference to provide some evidence for a given statement becomes one of actually changing the respective text. This is simply not necessary if citation references are seen as meta-information super-imposed on the text, without any influence on sentence structure, that can be skipped while following the flow of the text, unless the reader specifically looks for references.
In general, I consider in-text citation references as an artifact from the days when scientific publications were still text printed on paper. We have various of these artifacts, such as papers being nailed down layout-wise on a fixed-size paper format like PDF, with what seems like physical page numbers and fixed-format section numbers, rather than per-document page numbers1 and a semantically nested structure of sections and subsections (that just imposes order and hierarchy, but not superficial things like numbering style). In my opinion, citation references are exactly this - an artifact that, sooner or later, will disappear and be replaced with meta-information embedded in the document, used by viewers to provide on-demand source information (e.g. upon mouse-hovering over the passage of text based on the cited work, which otherwise just contains a subtle visual cue indicating that there is something more embedded there), similar to context-aware editing helper popups found in some code/text editors:
In my opinion, citation references are like these context-aware popups. They are displayed near the text they refer to, but they do not belong to the text flow (and wouldn't be read out when reading the text of the actual document).
One additional possible issue when treating citation references like words is the fact that citation references in some styles just do not look sufficiently like words to be treated as such. One such style is used in another question, and the examples in the question illustrate themselves that citation references in superscript do not look nice as words:
However, in⁴ only a small uncertainty has been introduced ...
This is partly coming back to my aforementioned statements - ideally, the appearance of citation references should not be nailed down by the document, and consequently, citation references should be inserted in a way that will essentially work no matter how citation references end up being styled in the final document.
1 Things are beginning to change, as evidenced by a question here, and also some publishers that give their papers page numbers of the style