That is by design. The bold, italics, bold italics, franktur, sans-serif, monospace, script, double-struck, etc “Mathematical Alphanumeric Symbols” have specific meanings, even if on the surface it looks like merely a difference in presentation.
Page 810 of the Unicode Standard (version 12.1)
The letterlike symbols include some of the few instances in which the Unicode Standard encodes stylistic variants of letters as distinct characters. For example, there are instances of blackletter (Fraktur), double-struck, italic, and script styles for certain Latin letters used as mathematical symbols. The choice of these stylistic variants for encoding reflects their common use as distinct symbols. They form part of the larger set of mathematical alphanumeric symbols. For the complete set and more information on its use, see “Mathematical Alphanumeric Symbols” in this section. These symbols should not be used in ordinary, nonscientific texts.
And, the MathML specification, section 7.5: Mathematical Alphanumeric Symbols clarifies even further:
A MathML processor must treat a mathematical alphanumeric character (when it appears) as identical to the corresponding combination of the unstyled character and mathvariant attribute value. It is important to note that the mathvariant attribute specifies a semantic class of characters, each of which has a specific appearance that should be protected from document-wide style changes, so the intended meaning of the character may be preserved. The use of a mathematical alphanumeric character is also intended to preserve this specific appearance, and so these characters are also not to be affected by surrounding style changes.
Meaning, these stylistic variations exist for solely for their functional differences. This is also the reasoning behind the existence of any subscript characters, outside of backwards compatibility with characters from existing code pages. The non-compatibility subscript characters that exist all have specific, inherent meaning. On the other hand, reproducing the US English alphabet for random usage (e.g. constructing words, footnotes, etc) would only be for stylistic difference since there would be no inherent meaning to each specific letter. This is why the preference for these purposes is to handle it via markup / font.
That being said, as someone who typically does not have the ability to specify markup for the situations that I deal with, I completely understand the frustration in not having complete sets of these stylistic variations. It’s quite the tease, especially with most of the ones that do exist not equating to the equivalent base English letters. At the same time, I get why Unicode doesn’t go down this road: they would have to offer similar variations for other scripts / languages, and that would get extremely messy.