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.