I wouldn't say there is a lot of excess fuel as a percentage of the mix in exhaust gases, but there is some, by design. Maybe a few percents. Why do we want so

I wouldn't say there is a lot of excess fuel as a percentage of the mix in exhaust gases, but there is some, by design. Maybe a few percents. Why do we want some fuel in the exhaust? Burning an oxydizer-rich mix is not a good idea, especially with a reusable rocket. You'll have a very hot gas that is going to burn-corrode your engine. Metals can burn in an oxygen-rich air. Now imagine that mix at 3,600 K and 300 atm pressure. You'll have what is called in the industry an 'engine-rich' burn. You don't want that. Also, I don't know about this rocket but sometimes you want to cool down your nozzle and you can do that with unburnt fuel that you inject from the side. Running a stochiometric mix puts you also at risk of damaging your engine (some parts of your mix might be oxygen-rich), on top of combustion temperature being higher. Now, burning a fuel-rich mix make these problems go away. And does not decrease much your thrust: heated at very high temperatures, this residual fuel will expand and contribute to some part in the force generated. Last, a fun fact: you can detect when then rocket leaves the upper atmosphere with the flame color! That's when the flame goes from being orange (high temp residual fuel meets oxygen from the atmosphere and burns) to being grey (flame meets the atmosphere but not enough oxygen to relight it, and soot is grey). You can clearly see it happen around 40km altitude here: https://youtu.be/xY96v0OIcK4?t=15881 https://youtu.be/xY96v0OIcK4?t=15881