I find that the issue with "leaving most used stuff on the cooktop" is what you do with it when you actually need to cook using different stuff? Where do you put it? So you still need to have the shelf/drawer space for it, even if mostly left "waiting".
Sure, if you have a very big 40"+ cooktop with 6+ cooking zones it is likely some will be available as "storage" space at all times. Over here mostly 24" class cooktops are the thing though. Meaning that while the kettle could stay semi-permanently on it and be put only sideways. That is about it. Sure, a pot and a pan IS there mostly, but those still need "their place" for situations when real cooking starts .. and that place should be quickly accessible.
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On another note, our plan for a new kitchen is to have three dual hobs instead of a single quad gas one as is the case today. A gas hob, an induction hob as the main ones and a cast-iron hob at the location there is just a put-aside space now. We figure the space is anyway "used" for placing pans and pots, so why not just "store/place" them on a cast iron hob that can be useful at times in its capacity and takes zero additional space, nor needs a consideration when placing stuff on, unlike the main gas and induction hobs do.
We had a cupboard with fixed shelves accessed through two doors so I put the shelves on slides and called it done.
I take it you do not cook that much complex stuff in the kitchen. A drawer behind doors cannot be practically accessed while one of your hands is occupied. Unlike simple doors (no need to open both of them) or a simple drawer could.*)
I find to have a blocked hand all the time /making dough by hand, cutting meat, holding something in it, whatever the cause/ so a one-handed operation for pulling the most-used stuff out is a must in my view.
*) That said, a face-less drawer in the form of a shelf on slides is probably not that bad an idea as the stuff on the front of it is still accessible without both doors opened. Rethinking it .. it is an excellent idea. Especially for an existing kitchen upgrade.