Status quo
Presently, if you want to make even slight changes to an existing theme, it is necessary to write a plugin/app for this alteration.

In order to lower the "barriers of entry" for non-developers and to de-clutter the amount of necessary plugins, it might be a good choice to introduce a template override/overwrite system.

Depending on the necessary resources, this might be applied either database of file based.
File based: have a custom theme folder that only contains changed template files (in original structure) and will never been overwritten by an update/upgrade. If this folder contains any altered files, deliver them - otherwise make use of default.
This way it would also be possible for theme vendors to offer adapted standard themes.