This is an idea that has been posted on r/MinecraftSuggestions a myriad of times, but I've never actually seen an implementation, so here it is. This mod makes chainmail armour turn invisible with the player when they use an invisibility potion, both giving the largely irrelevant chainmail armour a use and also buffing invisibility slightly so you can't get oneshot.
This mod can be used only on the server, and vanilla clients can connect and will not see chainmail armour on invisible players - however, players will still see their own armour all of the time and this may be confusing. Installing the mod on the client side as well fixes this.
Please report any issues on the github page on the sidebar.