When scanning over a network, the topology between the scanning software and the server you are scanning is very important.
Some tools need to be run on the server you are scanning.
Depending on the type of scan you are doing, some tools will require that you run them on the server you are analyzing. This is usually done in what is called white-box testing. By running the tool on the server, the tool will be able to read the source code of the application. An example of this kind of tool would be the Acunetix WP Security Plugin. This is a plugin that runs within your wordpress application.
Other tools should be run over the network.
You should position your tool so that it can reach your server similar to how your users reach your server. WPScan is this type of tool. For example, if your website is on a private intranet, you should be running your tools from an intranet connected machine.
Should I install wpscan on my wordpress server?
I can't see anything directly wrong with this. You should note that if you have load balancers or web application firewalls then your results from using WPScan locally may be different than if you ran them from another place on the internet. This can be helpful, as you may find vulnerabilities that your WAF may block, but still exist.
If you do have direct access to the server, you should look into white-box security solutions as well. White-box can often be more accurate since analysis can be performed directly on the code and not just on server responses.