Yes, lack of trisodium phosphate broke our last dishwasher. We didn’t realize it at the time. We also had to have a plumber repeatedly come in and clean out the drain pipes.
The problem is that real trisodium phosphate is hard to find. Some of the stuff that calls itself TSP is fake sodium phosphate. As you say, you need to check the box.
The whole business is truly stupid. Here in Vermont, we have our own well water, and our woods and pasture are almost always too wet. I don’t know why we should be forced to use less water because they’re running short in Arizona.