But now you have many more issues,
if you use a bitmap, it will look pixelated sometimes, some people love to zoom over text at incredible levels. What about light/dark themes?
If you use vector graphics, then which kind of them? will you use quadratic beziers, allow cubics? And don't think that it is easy to render vector graphics efficiently, there are many issues, parsing, anti aliasing, performance, you are also adding a new security nightmare, a good attack vector with complex to handle, parse untrusted user input.
And boy, we didn't even talk about caching, when will you send those payloads? when you type one emoji? Then what about the 2nd time? Surely not? Then how do you know the receiver has not lost your first payload? Should you batch send most payloads at the beginning? Will that introduce latency? Will you be hated by future generations?
Decoupling meaning, intent from representation, implementation is a good idea from text encoding schemes. We should not lost it. Fonts are a perfect example, most people are happy to use them. They do not overly complaint that you can change the way text is looking. The same meaning is sent to you, your platform text rendering stack is interpreting it and macos users are happy to have their consistent look, windows users are happy to have their ClearType legible rendering, ..well most are anyways.
Complex subjects rarely call for a simple hack. Yet I agree, emoji rendering is an issue. Some people even want to put in fonts rendering code (wasm?) because of how complex it is to handle.
And it is up to everybody how graphical representation of such encoding looks like.
Unique, universal and uniform encoding -> Unicode, in 1988 coined by Joe Becker.