Sadly, it wasn't it. 16 bits weren't enough, and stuff like the fact a Unicode rune ≠ printed character (i.e. [è] can either be a single codepoints, or a combination of a [`] modifier and the latin letter [e]) meant there was basically no point in using 16/32 bit chars in the first place. When people really understood this it was almost the '00s, and stuff like Python, Windows, macOS (due to NextStep), Java, .NET, Qt were stuck. It's impossible to go back to plain `char` without annihilating backward compatibility, so everyone kept using it internally.
Fun fact, some of those languages and frameworks I mentioned never bothered switching completely to UTF-16 - for instance, Python now uses a weird mixture of ASCII and UCS2 internally.