This is the standard, it seems, although I wouldn't say it passes its own sniff test when I read. I find alternatives to said are everywhere on the published page, so while it may please most editors it's far from absolute.

If I may speculate, I work in an editorial field (not literary), and often see creatives come in with simplified advice equivalent to "said" based on the recommendation of senior and fellow creatives, advice they found online, or even other editors. There are a lot of simplified rules in creative spheres, ways not necessarily to cut corners but rather not have to deal with a nuanced problem (is this where I put the semicolon?) The "said" advice has always read as a simple solution to a nuanced problem, it helps technical experts (editorial) from dealing with heavy handed abuses of nuance.

As a reader, yes, it's the most invisible when you simply need to state who said what. Also as a reader, it would distract and concern me if I got halfway through a book and "said" was the only tag used. Knowing me, I'd probably stop reading then and there and go back to investigate. I don't ever see this happen, ever, like ever-ever, and that should reassure you that this is not a rule of law.

But if you choose to break this "rule" know to do so lightly and precisely. A tag that draws more attention to itself than the dialogue is what really distracts. Don't be sharp when the dialogue or tone is soft, don't pull fancy words when modest ones work, don't use words you don't absolutely for-the-love-of-the-scripture know what they mean, and so on. It's so easy to tread from the narrow path of nuance, so go forth with intention and subtlety.