Let me preface this by saying that I have been a faculty member at a STEM-oriented, Ph.D. granting, university for 34 years and I have served in administration for significant time including 3 years managing the university’s graduate admissions operations. MEng degrees are generally treated just like other professional degrees such as graduate degrees in business, law school, medical school, etc.
As others have said, the MEng students at the most highly selective universities (I am guessing that this is what you mean by “top”) are considered cash cows for the engineering college and thus are the last in line for any TA positions. MS (thesis) are in front of them and PhD students are generally at the top of the list. It stands to reason that whether or not there is an official policy (and at my university, there is the policy that MS and MEng students can be hired for a job but the university will NOT foot their tuition bill), the MEng students are likely not to get a fully funded TA position. With highly selective PhD granting programs, the TA position is a way to subsidize the PhD program and research and since they are highly sought after, professional masters students are willing to pay the tuition costs as they feel it will help them get a higher pay after they graduate.
Yes, you might be able to find a research program willing to pay you as an RA but if you are a non-thesis program where research is not required, the mere fact that you are looking for a research position is not consistent with your stated educational objectives. As a professor, I would rather find funding for a MS (Thesis) student who might eventually switch to a PhD.
Yes we need more STEM majors but this means BS degrees, not necessarily MEng degrees and this is more a question of encouraging students to study mathematics and science in high school and apply to STEM programs in college. You have an Engineering BS already and the programs you have been admitted to are catering to students who feel that the MEng will provide them a better salary or a qualification that a B.S. does not. Statistics from the Council on Graduate Schools (I can’t find the document right now) show that the salary increase between a BS and a Masters is larger than that from a Masters to a PhD so that is why there is such a demand for the MEng. However, that is not necessarily the right option for a student just graduating with a BS. Generally, working for a while helps the student decide if an MEng is really necessary for career advancement. If it is, there will be a way to get it and it won’t necessarily require an investment of over $100k. At that time, you should be able to get into the same programs because your academics are still the same plus you have work experience.
Bottom line, while it is flattering to be admitted to all the these “top” schools for a MEng, realize that the admissions criteria are different than for MS (Thesis) and PhD because of the purpose of these programs, that is generating tuition revenue. If you can’t afford it then work for a while and perhaps your employer will pay for it later if you find that you need it or you might decide that your career will be just fine without an MEng.