I think actually you could. A thought experiment:

The problems with Unicode are mostly to do with internal inconsistencies and churn, problems that usually only affect programmers.

1. Different ways to encode the same visually indistinguishable set of characters as code points leading to normal forms, text that compares unequal even when it appears to be identical, the disastrous "grapheme clusters" concept and so on.

2. Many different ways to encode the same sequence of code points as bytes. Not only UTF-32/16/8 but also curiousities like "modified UTF-8".

3. Emoji. A fractal of disasters:

3.a. Updates frequently. Neither Unicode nor software in general was built on the assumption that something as basic as the alphabet changes every year. If you send someone an emoji, can their device draw it? Who knows! In practice this means messaging apps can't rely on the OS system fonts or text handling libraries anymore which is a drastic regression in basic functionality.

3.b. (Ab)uses composition so much it's practically a small programming language, e.g. flags are composed of the two letter country code spelled using special characters. People are represented as as generic person plus skin color patch, families are represented using composed individual people etc.

3.c. Meaning of a character is theoretically specified but can subtly depend on the font used, e.g. people use a fruit emoji in visual puns because of how it looks specifically on Apple devices, so a "sentence" can make no sense if it's rendered with a different font.

3.d. Unbounded in scope. There's no reason the Unicode committee won't just keep adding new pictograms forever.

3.e. Encoded beyond the BMP which in theory every correct program should handle but in practice some don't because nobody except a few academics used characters beyond it much until emoji came along.

3.f. Disagreement over single vs double width chars, can only know this via hard-coded tables, matters for terminals and code editors.

Some of these can potentially be cleaned up outside of the Unicode consortium in backwards compatible ways. You could have a programming language that automatically normalized strings to fully composed form when deserializing from bytes, and then automatically folded semantically identical code points together (this would be a small efficiency win for some languages too). You could campaign to build a consensus around a specific normal form, like how UTF-8 gained consensus as a transfer encoding. You could also define a fork of Unicode (using private use areas?) that allocates a single code point to the characters that are unnecessarily using composition today but don't yet have one and then just subset out the concept of composition entirely.

Emoji are a big problem. It's tempting to say that these should not be encoded as characters at all. Instead there could be a set of code points that define bounds that contain a tiny binary subset of SVG, enough to recreate the Apple pixel art somewhat closely. Emoji would always be transmitted as inlined vector art. Text rendering libraries would call out to a little renderer for each encoded glyph, using a fast fingerprinting algorithm to deduplicate the bytes to an internal notion of a character. To avoid wire bloat, text can simply be compressed with a pre-agreed zstd or Brotli dictionary that contains whatever images happen to be popular in the wild. At a stroke this would avoid backwards compat problems with new emoji, enabling programs working with text to be upgraded once and then never again, eliminate all the ridiculous political committee bike-shedding over what gets added, let apps go back to using system text support and get rid of the bajillion edge cases that emoji have spewed all over the infrastructure.