Bug introduced in 11 or earlier and persisting through 12.1
[...] I have filed a report to the development team, raising the issue to them. [...]
[CASE:3802659]
CellPrint[Cell["test", "Text"]]
CellPrint[Cell["test2", "Text", "MyStyle"]]
CellPrint[Cell["test3", "Text", "Text"]]
NotebookImport[EvaluationNotebook[], "Text"]
{"test"}
Since multiple style cells are officially supported I would consider it a bug. Or have I missed something?