My first reaction to the "no ties, no jeans" dress code was: what a great idea! After reading through this thread, I still think it's a great idea that works well to communicate a specific level of formality. As others have said, I would not interpret "no ties" to mean: "Absolutely do not wear a tie". Rather I would read it as "ties not required". If some people are more comfortable in a tie, they would probably wear a more casual one to an event like this. And not look out of place or overdressed.
For research purposes, when I was out for a run this morning with a friend, I asked her opinion. FWIW, we are both in our mid-50's and work full-time in professional positions. She in particular attends a large number of events that are connected with her job. Her reaction was, "Perfect! Just four words to convey the level of formality they're looking for!"
IMHO, using any qualifier on the word "casual" will still result in a certain number of people wearing jeans. And I think if the hosts don't want jeans in any way, shape or form, they have to specify exactly that. Note that I'm not expressing an opinion on the appropriateness of jeans for any event, or whether the hosts should make this distinction, etc. Just stating that because jeans of all levels of style/formality are ubiquitous in today's society, only a direct "no jeans" request will convey that they are not preferred attire.