Sure higher speed is good for local connections, but not so much otherwise.
For example, let's say you're filling up your gas tank.
Tank -> hose -> nozzle -> tank
If only so much is able to go through the hose, getting a bigger nozzle isn't going to get more gas through. By that same logic, you could say getting a bigger tank (keeping everything the same) would allow more gas to get through the hose/nozzle. This is of course not the case because the connection is still being restricted by the rest of the process.
Internet -> modem -> router -> devices
For example, let's say you're filling up your gas tank.
Tank -> hose -> nozzle -> tank
If only so much is able to go through the hose, getting a bigger nozzle isn't going to get more gas through. By that same logic, you could say getting a bigger tank (keeping everything the same) would allow more gas to get through the hose/nozzle. This is of course not the case because the connection is still being restricted by the rest of the process.
Internet -> modem -> router -> devices