The block chain came first. Originally chains were made of identical plates inner and outer. 3-4 plates were placed together with a pin through them with 1 plate on each side riveted on. The sprockets of the time had a 1" pitch because the teeth couldn't engage the block.

Later the laminated block was replaced with a solid block which was less taxing on the sprockets, and later yet that in turn was replaced with a block that had rollers. But these 1" pitch roller chains still had the spacing of 1" block chains with 2 roller spaced closely on what was the block, then a larger gap between links.

The last innovation, was respacing the rollers to have the uniform spacing of modern 1/2" pitch chains, allowing 1/2" tooth intervals.

Like with everything mechanical, it's an evolutionary process. 1/2" pitch was a necessary step that made derailleurs possible (or at least practical), but the 1" pitch standard hung around for decades for single speed applications, probably because the sprockets were already tooled and change cost money.