The universe is Einsteinian because otherwise e could not equal mc2.
And if that were the case then stars could not shine, and a TON of other things would not work. Atoms could not exist either.
The reason is that as you go faster you have more energy (obviously) and since you have more energy your mass increases. Since your mass increases you need even more energy to increase your speed (since now you weigh more).
Take that to the limit and you find that as you reach the speed of light your mass goes to infinity.
So it's necessary that it's impossible to exceed the speed of light - for example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). Then relative to each other they are going faster than light - which means they have more than infinite energy.
Can't do that.
So relativity is necessary if you want mass to be interchangeable with energy.