Yes, we have come close to reaching how fast the internet can be. The internet speed increase has started to plateau, and it will continue to plateau. It can only get so fast, and eventually we will reach a point where it can't get any faster. Instead of internet speed, our technology will advance in other ways that will make it easier to use.
I have found a free program called Ping Plotter which is pretty good at locating where the bottleneck in your network traffic is happening. They have a pro version with some extra features, but the free one has enough to trace the ping latency at each point along the way to whatever address you enter. Say you have it ping comcast.net. It shows you a plot of all the ip addresses that ping goes through to reach comcast.net, inluding your router. Nice way to trace the IP of some scam phishing site as well. I like the simplicity of the program and it always helps me figure out if the problem is on my end or the server's. Since I have a long coaxial cable running to my modem and it gets pinched from time to time, it has been a great troubleshooter.
Yes, today we can type and find content on the internet the same moment we think of it. What could be faster than that? In the beginning the internet was very slow and we could do many things while we waited for any page to load. Today we browse in a blink of an eye.
No, we are nowhere near the peak of internet speeds. Technology is constantly improving. Just 20 years ago, most americans still had dial-up internet. Today, the vast majority of americans have access to broadband or DSL quality internet. When computers were first invented, they filled entire rooms. Today, we hold computers in the palm of our hand.