Is it really that problematic though? I’m not disagreeing with you in that, yeah, sometimes, you can’t know what you don’t know. But, I just wanted to say to @Micha-kun and others like them: I think it’s fine for beginners (and non-beginners) to merely decompose the sentence and carry on reading. A lot of times, grammar elements have broad meanings, and then specific phrases acquire a specialised meaning, so you won’t be too far off.
といっても is totally transparent, but even in the case of てからというもの, even if you take てから as “since” and というもの as “the matter of” (some kind of weak thematisation, like a weak は), you’d get most of the meaning. You miss out on the idiomatic aspect, that maybe it’s more precisely the time/period since/after something, or that it’s usually directly adverbialised, but really, not that much IMHO… and actually none of that is made explicit in the JMdict entry either.
と at the beginning of a sentence followed by something that looks like いう? You know it’s likely a quoting particle before いう; it probably quotes whatever comes before, even if it’s a whole sentence with a period. で at the beginning of a sentence? It’s probably the gerund/te-form of だ, so you re-read the previous sentence as if it ended in て instead—it’s like how you can sometimes use だから instead of adding から to the previous sentence. And it’s similar to how in English we start sentences with conjunctions all the time: and, or, etc. Now and then, you’ll get tripped and things won’t make any sense, i.e., you see Xところが, think it’s “the place where X” marked with が and then nothing makes sense; in that case, yeah, tough luck. (There are quite a few of those noun+particle => phrasal conjunction, though, so you learn to spot the possibility.)
None of the above is perfect, and it’s just my two cents, anyway, but it’s good to keep your learning/reading in perspective.