Back to latency, to load this very forum page took 55 resources.
That means with 30ms latency on your connection you have 1650ms of latency just to establish the connections to the server to load each resource (not counting any DNS lookups).
Granted, pipelining and concurrency will reduce that time considerably, as much as 1/8 I believe, but then there is 30ms latency on each and every ACK packet too, which are sent to the server after each packet of information is received, to confirm you are ready to receive the next.
That basically means that for 30ms your connection is just waiting for the next packet of information to come in, for every single packet of information. Again, the fact you have multiple connections all slightly offset in time from each gives the illusion that your connection remains busy all this time, but it IS slowing things down subtly.
Now on a 15ms connection that is 825ms of latency to establish the connections and again half the latency for the ACKs, and so the data comes in quicker. The end result, the page loads faster. Its just simple maths.
That is why web pages can sometimes load faster on a low latency, low bandwidth connection than a high latency, high bandwidth one.
None of this of course takes into account the speed of your PC and monitor actually DRAWING the page, but I can tell a difference. It might not be the end of the world, but its there, and becomes much more relevant when your connection is busy as the higher the latency the more things will queue up waiting for a free slot to send/receive data.
You only need look at peoples pingtest graphs to see how when the connection is in use the latency goes up, the lower your latency started, the lower it is during use. Just compare my connection (the latter) to someone on lower latency than me. See how the yellow spikes mostly remain much lower than mine.
That means the chances of being able to keep decent enough latency to game, VoIP, etc, while still doing browsing/downloading are much higher when your latency is low to start with.
But my real point in all this is why put up with 30ms latency if you can get 15ms or lower?
Even if you do not notice the difference, doesn't it make sense to get the best connection you can for your money?