Can't say I have ever come across this behaviour, and it seems to work as expected for me.

What version of Umbraco are you using?

So I continued on, looking into this. And two things occurred to me.

1. We rarely put classes on the p-tags, often we want to color parts of the text, not that often paragraphs. So the classes will usually be on spans and not paragraphs
2. When copying text with parts of the text colored using spans, this coloring will be removed as well.

After diving into the source code, I found a setting on the TinyMCE RTE called "paste_process", which was calling a function called cleanupPasteData. This can be overwritten in appsettings.json under the RichTextEditor-property.

function cleanupPasteData(plugin, args) {

  // Remove spans
  args.content = args.content.replace(/<\s*span[^>]*>(.*?)<\s*\/\s*span>/g, "$1");

  // Convert b to strong.
  args.content = args.content.replace(/<\s*b([^>]*)>(.*?)<\s*\/\s*b([^>]*)>/g, "<strong$1>$2</strong$3>");

  // convert i to em
  args.content = args.content.replace(/<\s*i([^>]*)>(.*?)<\s*\/\s*i([^>]*)>/g, "<em$1>$2</em$3>");

}

appsettings.json - configuration:

"RichTextEditor": {
        "CustomConfig": {
          "paste_preprocess": "",
        }
      },

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