To answer the question in the subject — Both of my kids did both tests and yes we submitted information for both. Whether it was the “right” thing to do or required by the schools, I can’t really speak to. However, both did generally well on both tests (ACT a little bit better) and both did well in the admission results.
I will say sticking to SAT only is cheaper because you only have one fee to send all SAT scores (and subject tests) to a school. The ACT charges for each set of scores to a school. (And for engineering, you will most likely have to send subject tests)