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?