The current VPNs I am using are Express and Nord VPN, both of which are paid VPNs. In my opinion, using Express and accessing the recommended servers will improve internet speed somewhat but Nord does not.
VPNs do not improve your internet speed, that is a misconception. What they actually do is unblock routes on your router/network that are jammed due to some technical difficulty, by redirecting the traffic along a different path. So when before it would feel like your browser was just loading a site forever without connecting successfully, now with a (good) VPN, it would load very quickly.
You're right. But it's worth noting that in some countries, this may not only be due to technical difficulties. For example, some regulators may intentionally slow down connection speeds to a particular site because they may not like it for some reason. It can be a gambling site or any other undesirable site. In this case, VPNs really “speed up” the connection, and are actually the only tool for those people who want to get access to a more or less uncensored internet connection.
What you said it correct, and what the other user said Is correct too, so, let's just say that the both of you are correct, VPN actually does more internally than we all can actually see or take notice of.
Believing that VPN doesn't improve internet speed is the real misconception, because looking at it critically, when for what ever reason(s), networks jammed or there is a kind of error somewhere which lead to connecting to a site becoming way slower than normal, and the user turns on a VPN which managed to fix the slow connection, what do we call or assume that to be?, of course VPN has helped that user speed up the connection to his or her favorite site, and of course the example you gave is also very legitimate.
But however, one question I want to ask is, is it possible for someone to connect his or her VPN to the same network in a country where he or she resides? Like for example, I live in Nigeria, and I want use VPN to visit a site, is it possible to connect my VPN network to Nigeria? Will there be any difference if it's possible to do?