Due to the extensive amount of integration needed to transform SharePoint into an industrial-strength extranet platform, ExCM has been built as a custom SharePoint Farm Solution. SharePoint Farm Solutions offer the broadest and deepest range of development options when it comes to extending out-of-the-box SharePoint.
Farm Solutions that you have installed in your SharePoint Farm can be viewed on the Solution Management page in Central Administration (Central Administration > System Settings > Farm Management > Manage Farm Solutions) :

Like most custom SharePoint Farm solutions, ExCM consists of many different custom components that are added to your farm to enable its functionality.
The types of components that ExCM deploys to your SharePoint farm includes:
The deployment of these components (or copying them out to each server in the farm) is handled by SharePoint's native Farm Solution Deployment Timer Job. When you deploy a custom Farm Solution to your farm, this Timer Job unpacks the Farm Solutions file (which is a .wsp file, and essentially is just a cabinet file) and reads the contained "manifest.xml" file to know where to deploy each of the components in your farm.
Microsoft has designed the Farm Solution Deployment Timer Job to deploy the components of a custom Farm Solution ONLY to servers in your farm that have the Microsoft SharePoint Foundation Web Application service started:

If a server in your farm has the Microsoft SharePoint Foundation Web Application service stopped, the Farm Solution Deployment Timer Job will bypass that server.
Therefore, since ExCM adds new components to Central Administration (see in the list above) the only way that those components will ever be successfully deployed to Central Administration is if one of these conditions are true:
OR,
In some documentation on TechNet for SharePoint, Microsoft advocates not running Central Administration on a WFE and not starting the Microsoft SharePoint Foundation Web Application service on the CA server. Unfortunately, that guidance will not work in a scenario where you need to deploy a custom Farm Solution that installs custom components into Central Administration.
Microsoft acknowledges this fact in this text on another TechNet page titled "Plan service deployment in SharePoint":


Here some other articles on the web that discuss Farm Solution deployment and this particular issue in more detail:
By a well-respected SharePoint consultant:
By a well-known Microsoft engineer (this article is not specifically about this particular case, but points out the root cause of the issue - which is the SharePoint out-of-the-box Farm Solution deployment architecture):
Finally, in SharePoint 2016 & 2019, it is notable that Microsoft automatically starts the SharePoint Foundation Web Application service on ALL servers in a SharePoint Farm that is managed by the new MinRole feature. See these pages on TechNet for more details:
Overview of MinRole Server Roles in SharePoint Server
Description of MinRole and Associated Services in SharePoint Server
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