Chain wear tools may have their place, but I bet if you tested every bike on the road a huge proportion would indicate a change is needed when the chain could run perfectly well for thousands more miles.
The thing is, the new chain makes a big difference, and it's not just my imagination because it's new. The gear changes are smoother and quieter, evidence, to me, that a worn chain is detrimental to the performance of the bike. I'm not a performance cyclist, per se, but when you know something is clunky and worn, it's not a bad idea to do something about it. Probably quite a few cyclists wouldn't know or care. I know I could have run the old chain for longer, clunking its way from one cog to the next but I prefer to have it right. Hopefully this new chain will last for a few thousand miles.