Is it good idea to parent script to the game?

I have made custom module for replacing the TweenService, now i want to access it and i got a very cool idea to make it very easily accessible from multiple scripts, i want it because i want to feel like it is the real service and real services you don't get them like this:

local tweenService = replicatedStorage.modules.container.otherstuff.......

But like this:

local tweenService = game:GetService("TweenService")

So my shorter idea was to parent it to the game

script.Parent = game

I could create module which would do that in studio as you can't parent it to the game in explorer but the question is, is it good idea or should i forget about it, no, trash idea?

Thanks, kirda