That’s not true. While there have been fads in the past that some logos adhered to, the history of insignia is overflowing with what we would today call logos that were not coats of arms.
Outside of military use and maybe some rare other state uses, there wasn't much insignia, and especially not much insignia that you would call a logo by today's application.
These came in many styles and had a lovely variety which sprang from the message the person wanted to send and what they thought looked cool.