Was it by design or accident?
Arbitrary choice, it's unlikely satoshi performed research about effect block propagation on different block time.
Partly that, but in the whitepaper, Satoshi did mention it as a measurement for calculation of RAM/disk space requirements. It can be that as arbitrary as "10 minute block time "is believed to be, it might really be based on the current hardware available of that time when he wrote the whitepaper.
A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.
https://bitcoin.org/bitcoin.pdf