I completely agree that it’s good to play in parts as best/accurately as you can, and then only go back and quantize if you need to. So depending upon how accurately you play, you may find none or only gentle quantization is needed, e.g., maybe start with 1/32 or 1/16 and increase the quantize strength from 0% to 100% (which I prefer to doing iterative quantization) until you get a feel that’s a bit more tight but not necessarily always on the beat. But I’m not talking about quantizing individual notes in the key editor because usually Cubase (and other DAWs) do a good enough job quantization wise (on a MIDI region with many events) that you can get some reasonable quantization w/o having to edit the timing on a per note basis.
Play in your parts as best you can just to get them recorded and into the project. Then go back and re-visit them with more of a “producer” hat on and focus on how all the parts hang together timing wise. For popular music, many people start with getting the rhythm of the drums and bass correct . Once these are together, they might go back and re-record the parts they played in to now be more in time with the drum and bass track, e.g., keyboards, guitar, etc. In this workflow people often end up cutting up the performance with a region for verse1, verse2, chorus1, bridge, chorus2, etc. - because they might want to play in (and/or quantize) the parts for chorus2 to have a slightly different feel compared to chorus1. It really depends upon the type of music you are doing and how picky you want to be about the timing and variation of parts.
What I often find is that I come back to a project after 1 or 2 days of not listening to it and conclude that I no longer like the timing of the parts in chorus2 and want to look at each (MIDI) region there to see what is going on with them timing wise including recalling whatever the quantization settings are for those regions. I find this is not straightforward to do in Cubase (so I filed a feature request for it, Display and set quantization parameters per MIDI region (regardless of track)).
Instead of having to hit the record button, do a take, and then hit stop - try using retrospective recording. Cubase is always buffering the MIDI events you play, and can save them at any time into the project - should not matter if you are playing back the project and practicing with playing other parts. You can turn that into real take I think by using one of the options/fold down menus in the track inspector where it asks you to insert retrospective recording into the track. Maybe you can set the buffer size in preferences but I’m not sure.