The emoji field does a decent job replacing the relationship icon (the one that shows the type of relationship, little arrow) with a selected emoji…but only manually.
There are two problems I have with the relationship icon:
They cannot be turned off, fields always display it, regardless the purpose or use of the field, in many cases we don’t want to see that relationship icon.
They cannot be replaced by an emoji automatically, the field is not available in rules.
Note: the ability of disabling the relationship icon alltogether, is related to the specific use of the field, for example for navigation, in which ideally the whole display of the field needs to be different, not only the relationship icon, see also
Changing emoji/icons for entities using a formula or rule is in the backlog. We plan to work on it this year and will share more details once available.