First of all, welcome! I may be prejudiced, but I think you have indeed come to the right place for answers.
My thought on "What are the downsides . . . to cooking steak, chicken, and hamburger in the microwave" is: None, if the customer doesn't mind eating meat-flavored rubber.
Most places I worked at (including as grillman) did not even have a microwave, or it was used only for emergency prep; to me that is simply not acceptable for cooking.
What should you do about it? First, how did your chef or supervisor teach you to cook the grilled foods? Were you told to cook it all on the grill, start to finish? Or to mark the food and finish it in a very hot oven? Either of those is fairly accepted practice. I find it hard to believe that you were told it's okay to nuke anything.
So how about going to your chef and asking for a "refresher" for you and the new guy? If your chef balks or questions you, I think it's perfectly all right to explain why you're asking. It's not snitching, it's making sure that you serve the best possible food to the customers.
(FWIW, some long-time line cooks get tired, and lazy; and unless they are supervised well, they will try to get away with all kinds of bad habits. Not all, and not even long-time, but a few.
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