People had been doing derivatives (at least sort of) before Newton and Leibniz, Cardano (sort of) used complex numbers before Euler, algebra before Galois, categories before Mac Lane.
But these people "connected the dots", as it were. It's not merely a trick -- it's a fundamental contribution.
The new mathematics at least could be initially tiny, and then the notation provides the leg work for huge forthcoming discoveries.
A few examples:
https://arxiv.org/abs/2303.08829 (ZX shows equivalence between approaches that used to be thought of as different)
https://arxiv.org/abs/1704.08670 (ZX shows how to find new ways to implement fault tolerant operations)
https://arxiv.org/abs/2206.12780 (using ZX to build a 4-body parity measurement out of 5 2-body parity measurements instead of 6, and to show the previous constructions are easily related)
The fully expanded coordinate version is based on an arbitrary choice of spacetime coordinates.
Ideally you'd use a computer language/environment with a rich enough basic formalism to let you write the 1 formula in a human-legible way and have your compiler expand out all of the coordinate version as appropriate for the particular problem for the sake of doing floating point arithmetic.
Einstein tensors are a great example of notation as an enabling technology - it’s a mistake to think we have thought of all the notation tricks we might need.
I wonder if, for example, in attempting to reason about neural networks in terms of ‘gradients’ and ‘matrix operations’ we might look, to future mathematicians, like poor ancients struggling to handle arithmetic without a clean notation for rational fractions…