Many of the things you want to eliminate are actually important for answering this question in the real world. In practice, image quality almost never comes down to sensor characteristics. I'm a little reminded of this Monty Python sketch..... when you eliminate all of the image quality factors other than the sensor, sure, the sensor is the only spec left.
You mention the processing pipeline; this does matter in a sense, because there are factors like analog-digital conversion and possible noise introduced at other levels, but again, in a practical sense, this is all what you get when you read, for example DxoMark's sensor scores — the sensor in a lab is irrelevant, so sensor quality generally means the entire pipeline associated with the sensor, too.
When it comes right down to it, the most important image quality factors are, roughly:
- The lighting
- How the photographer responds to that — composition, technique, and other technical choices
- The lens and what capabilities it allows — especially in extreme situations
- The post-processing options selected by the photographer (including in-camera JPEG options if so chosen)
- sensor-related factors
And, crucially for the purposes of this question, it's important to note that if you buy any camera today above the bottom of the barrel — that is, anything with a 1" sensor or larger, or even a smaller-sensor camera in the higher end of that range — the image quality factors from everything sensor related range from A plus to A plus plus plus. They're all really good. Resolution, dynamic range, color rendition — wow. So, unless you have all of the rest nailed, the differences come out in the wash.