> An opinion that’s largely held by programmers and not people who actually do maths.
The "people who actually do maths" will almost by definition exclude anyone who has issues understanding the notation. You need to look at the latter group of people to work out if the notation is unnecessarily obtuse.
> it’s honestly so, so much worse. It’s multitude more verbose and so much harder to grasp.
As a counterexample, consider the proof that undirected Hamiltonian cycles is NP-complete, by reduction from directed Hamiltonian cycles. Karp's original paper says literally just this:
N = V × {0, 1, 2}
A = {{<u,0>, <u,1>}, {<u,1>, <u,2>} | u ∈ V} ∪ {{<u,2>,<v,0>} | <u,v> ∈ E}
By contrast, a vernacular English description would look like this:
Replace every node in the directed graph with a set of three nodes in a line. Gather all the incoming edges to the first node, and all the outgoing edges to the last node. Every path that visits every node exactly once must reach the middle node by starting at the first node and going through to the last node, and thence to the first node of a corresponding subsequent node, so every Hamiltonian path in the undirected graph is a Hamiltonian path in its directed counterpart.
More verbose, yes, but (IMO) easier to grasp.