The point of avoiding tags is to improve the ergonomics: you don't have to remember tag names, use a separate delimiting syntax anyway to indicate where the tag name is, and then repeat the tag name when you close the block. Especially given that this is for a block-level construct anyway, simply using a bracketing syntax isn't causing any of those problems.

Indenting inline code requires a text editor that makes indentation ergonomic or else extra effort per line; and it doesn't mesh well with lists or block quotes.

Well, if you want complex things like nested code blocks, then a kind of "tag" approach can be just the solution needed. Input-wise it doesn't really make a difference, whether I have to type "[[[" and "]]]" or "```" and again "```". Whether or not my idea is more like a tag doesn't seem to have any repercussions. Outsourcing ever more complexity into the parser, with bad design decisions however has a significant cost, which is making development of parsers and grammars difficult.