"Strong Pokémon. Weak Pokémon. Those are just the selfish perceptions of humans. You should try to win with your favourites." - Karen, Johto Elite Four
Shiny Pokémon can be very special. Despite the recent surge in shinies thanks to increased odds in-game and more accessibility with the GTS and wonder trading (which has gifted me most of my collection), a shiny Pokémon that we find randomly or intentionally breed for can end up becoming a more valued member of the team. If it's just for in-game play, I don't think you need to worry too much about a competitive team, you could probably beat the game with 6 Unown.
If you're putting a competitive team together, Raticate won't last long against Pokémon with much better base stats and pools bred for IVs, and it's too high a level for a FEAR tactic (I think). Economically, based on my own experience using the GTS, shinies are worth more than most legendaries. You may as well keep it, it will struggle in competitive play but can hold its own against the Alolan Elite Four with a good set.