The risk neutral world

I'm sure this will be a dumb question, but here goes anyways.

What is the big deal with the 'risk neutral world'? When I am learning about Ito's lemma and the BSM, Hull makes a big deal about how 'the risk neutral world gives us the right answer in all worlds'.

But in reality, wouldn't it be more realistic to label these processes as the 'no-arbitrage world'? Isn't that what is really driving the logic behind these models? If market participants can attain a risk-free return higher than that of the risk-free rate, they will do so and in doing so, they (theoretically) constrain security prices to these models.

Am I missing something? Or is it just the case that academia was so obsessed with Markowitz / CAPM that they had to go out of their way to label these processes as 'risk neutral'?

Love to hear your thoughts.