This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.
What you say is not a rebuttal of the parent comment. Parent explicitly said that average block times are 10mins in the assumption. The most recent block time doesn't change that.
Of course it doesn't speed up your own time, since you have perfect information about your own hashpower. But it does tell you information about the total hashpower that's online, statistically.
I'll give an extreme example to make this clearer. Suppose 10X hashpower just came online an hour ago. It's quite likely that ~60 blocks have been found in the last hour, assuming the difficulty adjustment hasn't happened since. Seeing this, one could deduce that hashpower went up by ~10 and that the expected time till next block is roughly 1 minute instead of 10.
Now, in most cases hashpower doesn't change that drastically but it remains true that recent block times give you more than 0 information about hashpower and therefore about the expectation for future block times.
