There is nothing wrong with using stranded wire in a transformer. I suspect the people who manufacturer transformers for a living mostly use solid wire due to cost and also the extra cross-sectional area that having insulation on each strand of stranded wire, which would make the transformer physically larger.
Someone probably makes some, but I have never seen a stranded wire that had the enamel applied AFTER winding the strands. There is Litz wire, but the individual strands are insulated so each one contributes to the cross sectional area.
So, if you are messing around and want to re-wind a transformer core with stranded wire, go for it. Have fun!