Unicode agrees:

> Several letterlike symbols are used to indicate units. In most cases, however, such as for SI units (Système International), the use of regular letters or other symbols is preferred.

> In normal use, it is better to represent degrees Celsius “°C” with a sequence of U+00B0 degree sign + U+0043 latin capital letter c, rather than U+2103 degree celsius. For searching, treat these two sequences as identical. Similarly, the sequence U+00B0 degree sign + U+0046 latin capital letter f is preferred over U+2109 degree fahrenheit, and those two sequences should be treated as identical for searching.

(From https://www.unicode.org/versions/Unicode13.0.0/ch22.pdf)

The why include the symbols in the first place? Just in case?

It's most likely for round-trip compatibility with another encoding. There are many Unicode codepoints that simply represent combinations of other codepoints. If you don't care about round-tripping, just normalize everything to NFKC or NFKD (the difference being that accented letters like á are one codepoint in NFKC and two codepoints for the base letter and combining mark in NFKD).

For lossless round-tripping with legacy character sets. This is one explicit design goal of Unicode.

So we can make search that tiny bit more complicated.