In some cases I'd argue, as an engineer, that having no calculator makes students better at advanced math and problem solving. It forces you to work with the variables and understand how to do the derivation. You learn a lot more manipulating the ideal gas formula as variables and then plugging in numbers at the end, versus adding numbers to start with. You start to implicitly understand the direct and inverse relationships with variables.
Plus, learning to directly use variables is very helpful for coding. And it makes problem solving much more of a focus. I once didn't have enough time left in an exam to come to a final numerical answer, so I instead wrote out exactly what steps I would take to get the answer -- which included doing some graphical solutions on a graphing calculator. I wrote how to use all the results, and I ended up with full credit for the question.
To me, that is the ultimate goal of math and problem solving education. The student should be able to describe how to solve the problem even without the tools to find the exact answer.
Psi is used a lot in engineering. But honestly, pressure units are a bit of a mess. The metric unit is a Pascal, which is fundamentally defined as a Newton per square meter – unsurprisingly, that is an incredibly small quantity of pressure. It’s roughly 101,500 Pascals for standard atmospheric pressure. You’ll typically see pressure written in either kPa, MPa, or bars (1E5 Pascals) within a metric framework. For perspective, it’s 14.7 psi (lbs per square inch) for an atmosphere.
And personally, I think all of these are pretty silly when we could be using 1 atm instead, which is literally defined as standard atmospheric pressure. It’s a much easier way to visualize and intuitively grasp pressures.
BTU is another fun one. It’s the energy needed to raise 1 lb of water by 1 degF. Calorie is the energy to raise 1 g of water by 1 degC. Both are very pragmatic definitions and have a degree of intuition. Then they’re the metric unit, the Joule, which suffers from the same issue as Pascal. It’s the work done by a 1 Newton force pushing an object 1 meter. Once again, pretty small.