Translation is hard precisely because semantics is carried by syntax -- when the syntax is radically different, you can only approximate the higher order structures.
If semantics were actually distinct and carried by both languages, you could translate without that loss of subtle meaning.
I also completely disagree with your last sentence: semamtics could easily be syntax that has rules which are hard to compute.
NLP has trouble with long-range (or broad) effects, which are (some of) what I mean by higher order syntax.
Syntax is usually used to describe those rules of a language that are easy to compute; so easy that you don't have to understand the meaning (semantics) to do it. E.g. you can point to a missing semicolon in a C program without understanding what the program does.
Of course you can call the rules of well-formedness "higher-order syntax" in the sense that the computation required to decide it is of a higher order than syntax, but the distinction between syntax and semantics is by no means unnatural. It has been discovered independently several times; some ancient studies of the syntax of Sanskrit have survived to this day.
If semantics were actually distinct and carried by both languages, you could translate without that loss of subtle meaning.
I also completely disagree with your last sentence: semamtics could easily be syntax that has rules which are hard to compute.
NLP has trouble with long-range (or broad) effects, which are (some of) what I mean by higher order syntax.