Going back to the topic of real time image rendering, something important has been left out. All the posts makes it sound like real time rendering is better, but is often ignored because it's easier to pre render. While that isn't wrong, it's not the entire truth either and there are reasons to choose pre rendered even if you have the skills and time for real time rendering.
The most obvious is hardware requirements. Real time rendering requires GPU hardware fast enough to handle the task. A still image can pretty much run on anything. Adding assets to handle 3D rendering at realtime can easily result in using a lot more disk space too.
However a lot more can go wrong if you rely on real time rendering. If you say update an asset, say a dildo, then you need to go through every single scene where it is used because it might have introduced clipping issues. This will never be a problem for still images. As such real time rendering is easier to break and will require more testing of already finished scenes.
Putting more demand on the end user system, it becomes easier to encounter compatibility issues. Games in general can end up with objects being too large due to driver issues and similar. This is particularly a concern for commercially released games where people paid for them and have a right to support and/or money back if it is broken.
While 3D realtime rendering has become fairly good by now, for years 3D real time rendered visual novels had a really bad reputation because they looked awful compared to 2D drawn art. This is still valid in the sense that somebody can go out and buy a 4090 and allow each image to take up to 5 minutes to render. The quality from doing that will blow any real time rendered image any day.
It's also worth adding that Ren'py's simplicity isn't just good for end user runtime. With less stuff to set up, writing a game is faster. As such the current approach for The Headmaster is good for development speed (despite what some people say). Switching to rendering everything real time can easily result in slower progress. It will likely also require more pre-existing knowledge regarding how to work with graphics, so it can result in downright pauses while graphical issues are being studied.
Overall real time rendering would likely be a good thing, but people wanting it usually aren't aware of all the tradeoffs. I for one is perfectly fine with the pre-rendered setup despite having the hardware to do real time rendering.
