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This answer to How to write functional chord symbols with accidental roots, basically claims that (and I paraphrase) "#i is not a thing" in functional harmony. But why not just call a spade a spade, so to speak. If the chord is built on the raised tonic, why not call it #i, which is perfectly clear?
For example, in C major, why not call C#-E-G #io, which is completely clear, rather than adding the complexity of calling it viio/ii or some such?
Allowing for the possibility of a circumstance where #i makes sense, it would be the rare exception when applying an analysis in terms of functional harmony.
If the goal is just to name a chord, #i/I makes perfect sense. It's obviously a chord built on the raised tonic, and any added figures will express the type of chord and inversion. In the key of C major, say, #io obviously means #C-E-G.
In effect, using #i/I would simply be a variation on the Nashville Number System, which labels chords based on their interval relative to the tonic and does not concern itself with functional meaning. In such a system, #i/I or bii/II would be interchangeable, since they would point to exactly the same (enharmonically equivalent) chord.
The purpose of RNA is not just to name chords, but to name them in such a way as to describe how they operate within their specific musical context. To that end, there are established ways to describe chords and established ways to interpret RNA notations. Within this system, unlike the pseudo-Nashville example above, #i and bii would designate different and unique chordal functions for the same set of absolute pitches.
One of the fundamentals of RNA is that i/I chords — that is, any chord using Roman numeral i/I — carries a tonic function. #i/I has no tonic function within the "key of i/I". Such a chord would not feel at rest within the prevailing key.
While #i/I has no established functional meaning, the enharmonically equivalent bII does: it functions as pulling toward the tonic. When one sees bII, there is a likelihood that the following chord will be i/I, barring an exceptional circumstance. bII is often labeled N just to avoid any possibility of ambiguity of function.
Similarly, seeing the chord symbol viio, one immediately understands the likelihood that the next chord will have a root a half-step higher. This is why diminished chords with other functions, such as a common-tone chord, receive other designations, such as CTo.
In absolute terms — say, in "pseudo-Nashville" terms — this is perfectly clear. In C major we would have c - c#o - d - G. Perfectly common and easy to understand for anyone having seen the progression once or twice. In this way, the progression could also be given as i - biio - ii - V. Exactly the same progression, and just as clear.
However, such a notation is ambiguous as to chord function. For example, is the diminished chord leading upward or downward?
For this reason, the #i chord in this progression would be unambiguously labeled as viio/ii, because its function is to lead into the ii chord. It's function is defined as more strongly related to the ii chord rather than the i chord.
RNA is designed as an analytical language, and the complexity of the notation stems from the added functional meaning rather than the simpler literal designation of the chord.
