The situation sounds similar to ones years ago for statistics, operations research, optimization, and management science.

I view all of such work as applied math.

My experience is that applied math, from the fields I mentioned and some more recent ones, and more, with emphasis on the more, can be valuable and result in attention, usage, and maybe money.

I've had such good results and have seen more by others.

Some examples:

(1) Airline fleet scheduling and crew scheduling long were important, taken seriously, pursued heavily, with results visible and wanted all the way up to the C-suite.

(2) Similarly for optimization for operating oil refineries: So, here is the inventory of the crude oil inputs and the prices of the possible outputs. Now what outputs to make? The first cut, decades ago, was linear programming, and IBM sold some big blue boxes for that. More recently the work has been nonlinear programming.

(3) The rumors are, and I believe some of them, that linear programming is just accepted, used everyday, in mixing animal feed.

No surprise and common enough, IMHO what really talks is money. If can save significant bucks and clearly demonstrate that, then can be taken seriously.

But from 50,000 feet up, tough to get rich saving money for others. If they have a $100 million project and you save them $10 million, then maybe you will get a raise.

What's better, quite generally in US careers, is to start, own, and run a successful business. If that business is to supply the results of some applied math, and the results pass the KFC test, "finger lick'n good", then charge what the work is worth.

Maybe now Internet ad targeting is an example.

I'm doing a startup, a Web site. The crucial enabling core of what I'm doing has some advanced pure math and some applied math I derived. Users won't be aware of anything mathematical. But if users really like the site, then it will be mostly because of the math. So, it's some math -- not really statistics, operations research, optimization, machine learning, artificial intelligence, or management science -- it's just some math. The research libraries have rows and rows of racks of math; I'm using some of it and have derived some more.

Generally I found that the best customer for math is US national security, especially near DC. E.g., now some people are building models to predict the growth of COVID-19. Likely the core of that work is continuous time, discrete state space Markov processes, maybe subordinated to Poisson processes. Okay: One of the military projects I did was to evaluate the survivability of the US SSBN (ballistic missile firing submarines) under a special scenario of global nuclear war limited to sea -- a continuous time, discrete state space Markov process subordinated to a Poisson process. Another project was to measure the power spectra of ocean waves and, then, generate sample paths with that power spectrum -- for some submarines. There was some more applied math in nonlinear game theory of nuclear war.

Here's some applied math, curiously also related to the COVID-19 pandemic: Predict revenue for FedEx. So, for time t, let y(t) be the revenue per day at time t. Let b be the total market. Assume growth via virality, i.e., word of mouth advertising from current customers communicating with remaining target customers. So, ..., get the simple first order differential equation, for some k,

y'(t) = k y(t) (b - y(t))

where
the solution is the logistic curve which can also be applied to make predictions for epidemics. This little puppy pleased the FedEx BoD and saved the company. Now, what was that, data science, AI, ML, OR, MS, optimization? Nope -- just some applied math.

I have high hopes for the importance, relevance, power, fortunes from applied math, but can't pick good applications like apples from a three.