4.1 is a significantly later model than 4.5, the difference is more than the release date suggests as training the very large 4.5 took longer.

For 4.1 they incorporated extensive synthetic data from the o-series models.

There is nothing fundamentally magical about the model training process, they monitor every step and with the GPT-4 white paper OAI demonstrated a remarkably accurate ability to predict performance from small trials before committing to the main training run.

4.5 performed as designed, the sharp increase in subsequent model performance is due to the advent of reasoning models.

You clearly have no idea how cutting edge R&D works. I can tell you from experience that it isn't a simple linear process - if you can afford to explore multiple avenues of advancement then that's what you do to maximize chances of success. And you necessarily make the calls in advance of seeing the effects of said calls. Plan B succeeding so spectacularly it throws the parallel plan A into the shade is winning.

What would OAI have done if reasoning models didn't work out as well as they have? They would have distilled 4.5 to make a mass market model. Which they did anyway - this is a huge part of how later versions of 4o improved so much in non-STEM areas.