What Paul Ehrlich/Sandra Kahn, the Mews, Dr. Ann Mare Cole, and many others believe, is that proper oral posture is supposed to develop naturally in children given the right environmental circumstances. Mainly:

- Sufficient chewing and usage of the jaws while growing up (meaning a diet that does not mostly consist of soft food rich in calories, which results in little chewing and small forces being put against the jaws daily). The Mews have estimated that we chew about 3-5 % of what humans used to do before the "soft diet" revolution.

- Sufficient breast feeding followed by a clear transition to solid foods. Professor Paul Ehrlich explains in this video why this is important:  https://www.youtube.com/watch?v=tnOtQDVAP7I&t=206s

- Lack of issues preventing nasal breathing (such as allergy issues resulting in clogged noses). When nasal breathing is hindered open mouth breathing ensues, this results in open mouth posture with the tongue not resting against the roof ot the mouth.

- Proper nutrition.

So if you just make sure your kids chew sufficiently and that they can breath well through their noses you are more than halfway there. This will make your kids lives easier and less stressful since they will develop better and breath better.

So the way I see it it is not about being strict and causing stress for children (and I actually think it is quite silly of Mew to focus so much on the whole "sitting straight while eating part"), it is about giving them the right environmental circumstances, in smart ways (for example by giving them a diet that is nutritious, tasty and requires plenty of chewing) so that they naturally develop closer to how our ancestors used to develop their nice maxillas (as fossil records indicate according to the people mentioned above).

As Ehrlich points out (see: https://news.stanford.edu/2018/04/10/paul-ehrlich-problems-modern-jaw/), it may be wise to encourage kids to chew more gum if the parents can not change the diet to include sufficient amount of food that requires plenty of chewing. Having your kids chew some tasty sugarless gum for some time every day should most likely not be that hard to achieve.

I fully agree that it is important not to stress children. The way I see it it is about trying to give them the right circumstances in smart ways.

I don't see why you couldn't teach them about the importance of tongue posture and nose breathing without getting them paranoid about their looks. Just tell them "it's to make you grow up big, strong and beautiful" or something like that.