How to mod android rom so none can ever install an app in it?
Your idea of removing the store and package installer should work.

To do so, delete the following apks (and any .odex files of the same name) from /system/app, either in your ROM image or after obtaining root.


DefaultContainerService.apk - used for app installs by both the Play store and Packageinstaller.
PackageInstaller.apk - This is used to install non-market apps.
Vending.apk - This is the Play store.
Phonesky.apk - This is the Play store on JB and some ICS builds.


With those gone (and the phone unrooted), it should be impossible to install anything.

Note : I have not tested this.  Making a backup before doing this would be advisable.