Regarding the plastic container concern. I use Ziploc microwave containers which are made for microwave use. There is no hazard with these containers. There is a hazard using plastic containers not designed for microwave use, however.

The reason the chicken does not come out rubbery is that it is not done on high power. High power cooks the chicken too quickly and tends to overcook it. The timing and settings
I used for the above recipe was for about 2 pounds of chicken breasts. It is essential to work out your own timing for the amount of chicken you are cooking. Use an instant read meat thermometer…cook to 165 degrees and let the chicken sit covered for 5 minutes or so. The chicken will keep cooking and rise to the approved 180 degrees.

Another reason the chicken does not get rubbery is that at the last stage of cooking it is in chicken gravy which helps prevent overcooking.

The main secrets are using the right containers and lower power levels, I frequently use these same methods to make chicken soup. Using the right power levels, I can make a quick soup or one that simmers slowly for hours as if it were in a crock pot. That’s a recipe for another day though. I do hope I have answered your concerns and have helped you look at your microwave in a new way.