I don't think that "NMT and similar techniques" ignore meaning by design though. What they do do by design, compared to expert systems etc, is avoid having explicitly encoded knowledge (of the kind SHRDLU had). Take word2vec for instance, it's not NMT but fits into the "statistical NLP" description - its purpose is to find encodings of words that carry some semantic content. Now, of course it's very little semantic content compared to what an expert could plausibly encode, but it is some semantic content, and this content improves the (subjective human) evaluation of NMT systems that do use word2vec or something similar.
Also, we should carefully distinguish "prior knowledge" as in "prior common-sense knowledge" and "prior linguistic knowledge". The end-to-end trend eschews "prior linguistic knowledge", while current NLP systems tend to lack "common-sense" knowledge, for rather different reasons.
End-to-end training tends to eschew prior linguistic knowledge because it improves (subjectively evaluated) performance in real-world tasks - I believe this is true for MT as well, but an easier example if you want to look into it is in audio transcription. I don't think there's a consensus about why this happens, but I think it is something like - the previously way people were encoding linguistic knowledge was too fragile / simplified (think about how complicated traditional linguistic grammars are), and if that information can somehow be learned in the end-to-end process, that performs better.
Lacking "common-sense" knowledge - that's more in the realm of AGI, so there's a valid debate about to what extent neural networks can learn such knowledge, but the other side of that debate is that expressing common-sense knowledge in today's formal systems is really hard and expensive, and AIUI this is also something that attempts to generalize SHRDLU run into. But it is definitely incorrect to say that it's ignored by anyone by design...
BTW, the biggest improvements (as subjectively evaluated by me) I've seen in MT on "dissimilar languages" have come from black box neural nets and throwing massive amounts of (monolingual or bilingual) data at it, rather than anything from formal systems. I use deepl.com for Japanese-English translation of some technical CS material, and that language pair used to be really horrible in the pre-deep-learning days (and it's still not that good on google translate for some reason).