However, when encoding them into Unicode, the consortium suddenly discovered the importance of being frugal with character IDs and only defined a single "Han" sequence of characters for all three scripts. You need to select a matching font to actually display the text in the script that's intended.
This makes using those characters an unnecessary hassle and also came over as a cultural faux-pas to some (essentially like encoding Greek Eta, Latin H and Cyrillic En as the same character, because they look similar and the scripts have a common history)
<s>It also looks a bit hypocritical when Unicode otherwise goes the opposite way and has the space to encode dozens of variants of the Latin alphabet or — as we see here — several categories of dashes.</s> (Edit: Han unification was done when Unicode was still 16 bit, so there were real space constraints — so no hypocrisy actually)
Really, they needed to come up with the idea of variation selectors way earlier, and use them aggressively. And design something more consistent for character composition, and skip the precomposed characters (those really are glyphs representing a cluster; being able to treat the cluster as an atomic entity versus its components doesn't add actual semantic information to the text).