For my money, you have a good point—they should have explicitly said something about cover
To be clear, this is purely a matter of technicality. Under no circumstances should anyone rule that sending requires a clear path to the recipient—that would defeat the purpose of the spell utterly, as other answers have stated.
But that doesn’t change the fact that the rules, as written, don’t really spell that out. We’re left to infer it, on the basis that this limitation would make the spell too weak, and/or would make the unlimited range and cross-planar properties of the spell nearly meaningless. Which we should do, again, we should realize that all those things are true and rule accordingly, but the rules shouldn’t force us to make inferences like that. The rules state that a clear path is required unless something says otherwise, and in the case of sending, nothing quite says otherwise. It should.¹
So it’s an oversight. They forgot to say something because of the “obvious” purpose of the spell, or because of the assumed familiarity with the spell and its long history,² or because of any other editing error. It’s very difficult to notice what’s missing from the description of something you’re already very familiar with: your brain automatically fills in the blanks for you. On some level, part of the value Wizards of the Coast purports to provide you is having made the effort to counteract that tendency and actually thought through things. But on the other hand, the rules text is very large, and we don’t see a lot of questions about discrepancies like this. Mistakes are inevitable—they aren’t a reason to damage your game by implementing a poor rule.
To be totally clear, by “should” here, I mean “as written, the rules need a statement that sending does not require an unobstructed path as other spells do.” This is not merely “it would be clearer if they spelled it out,” this is “it is wrong the way it’s written.” “Specific beats general” cannot resolve this, because nothing in sending specifically addresses obstructions. Having “Range: Unlimited” or “across any distance” is not a “more specific” statement than “requires an unobstructed path,” they’re orthogonal statements about two separate requirements. Likewise, “even to other planes of existence” doesn’t tell us to ignore other obstructions. It is difficult to leverage these properties while needing an unobstructed path, but not impossible. Sending could be an unlimited-range spell, that can cross over into other planes, and yet still require an unobstructed path. It just isn’t, because that would make the spell worthless.
Sending is over 30 years old, and despite appearing in the core Player’s Handbook for every edition of D&D since 1989, it has never clearly stated that it ignores cover, even though this is the entire purpose of the spell and always has been. D&D 4e mentioned it could target a creature “anywhere on the same plane” (4e sending didn’t work across planes), but that was only as a result of a DC 40 Arcana check; lower check results give a range but don’t mention cover.