I've not done it, so I don't know where to look. You'll need to find the files that draw the menu and suppress it (bearing in mind you need to think about whether you want to cripple it globally or just for a set of projects). Then you'll need to think about all the other places you can create sub-tasks from.
You can disable it by disabling the relevant plugin component.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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