It's a very intuitive and concise solution for a real problem - but to cite someone more important than me on the syntax in question:
As for the points against the pitch:
The argument of more compact declarations ultimately leads us to re-add header files, and I wouldn't want that to happen.
Although splitting things into extensions is very common, this is just because some influencers like that style, and not because there's any evidence that this might be beneficial. I'd even say it's actively harmful, with SE-0169 as an example for fallout caused by same-file extensions.
Last but not least, no one would be forced to use the new syntax - and I don't think there's any danger of causing confusion.