You're wrong I'm afraid,
Shutting the kitchen door (and lounge) will be of a enourmous benefit should a fire develop in either of those rooms, shutting the door will keep the majority of the products of combustion in the room of origin, thereby making your escape
from the building safer and easier, the door is never a good enough seal to prevent the small amounts of smoke needed to activate the alarm from seeping by and activating it (think how little toast needs)
I'm telling you hand on heart that I have been into properties where shutting the door has at the very least prevented unnecersary damage to the entire property and has almost certainly enabled the family to escape the extremely dangerous smoke ( unburnt products of combustion) and leave the property.
Smoke detectors give you early warning to enable you to make a safe escape, it's harder or impossible to escape if you've gotta walk/ crawl through those toxic fume at 3 in the morning.
If you want further advice contact your fire and rescue service, ask to speak to their community fire safety department and they will tell you the same.
Al