Interesting paper. I work in fluid dynamics and tend to agree that computational power often is wasted.

To elaborate on a point not discussed in the paper: Many methods used in practical engineering won't necessarily converge to the empirically correct answer as the computational cost increases, say, by decreasing the time step, increasing the number of computational particles, and/or refining a grid. This is true even if the uncertainty is quantified. Without this guarantee, additional computational expenditure could simply be wasted. The problem isn't the lack of computing power, it's the model.

One reason is that "reliable" physics like, for example, the Navier-Stokes equations for fluid flows, are not being used as the model because the computational cost for solving those equations directly is far too high. Instead lower cost models are being used which may be loosely based on the reliable model, but ultimately is not the same thing. A numerical implementation of the lower cost model might converge to something (which is not necessarily right) as the computational cost increases, but converging to the right answer is less likely than the reliable model. It depends on the reliability and generalizability of the lower cost model and how well it has been tuned.

(To those familiar with computational fluid dynamics, convergence is one reason to prefer LES to RANS, though it's worth pointing out that not all LES methods are convergent.)

A hypothesis I have is that computing resources have caused many scientists and engineers' theoretical abilities to atrophy. Perhaps they were never that good on average to begin with, but in my academic field I work in theory partly because I've found so much low hanging fruit. I don't see much of a point in making expensive computational models if applying basic regression techniques with a simple theory-based model is similarly or even more accurate. These simple models are much more efficient.

Also: I wasn't aware of attempts to bound the results. I attended an uncertainty quantification seminar before and asked one of the lecturers about this more generally and they seemed skeptical of its utility.