In a modern home, there should be supply and return vents in every room. My home built in 1978 has 3 returns for the entire house, one on each floor. Master bedroom has a supply, but the return is located in the hallway. Over the years, the recommended door cut to allow air flow has been changed (presumably for greater privacy) - which leads to the scenario you're describing.
I could add the door cut back in, install return transfer grill, or look into adding a secondary heat recovery ventilator that acts independently of the primary HVAC system.
I know many people who put 'draft stop' devices on the bottoms of their bedroom doors in older homes (old enough to not have returns in each room, but new enough for central air), not realizing they're cutting off the one bit of circulation they need for a proper functioning central air system!
Or they buy new high efficiency windows and doors, and that 'tightens up' the house, but they don't also install an HRV (Heat Recovery Ventilator) to exchange outside air.
Realistically new windows and doors probably wont drop the homes air changes per hour below the recommended minimums, but I don't know for sure. I've gotten my crawlspace spray foamed and I'm getting my vented attic spray foamed to bring it into my envelope. Also getting new windows and doors soon, but after all of that I think enough air could leak through sill and top plates, electrical outlets, etc.
Having the foam crew do a blower door test for free if we go with them, so I guess I'll see. I live in climate zone 5a (cool, humid) so historically natural ventilation was used via induced pressure differentials generated by mechanical means (dryer, furnace, bathroom and kitchen vents). When we get new furnace and water heater that pull combustion air from outside, we're left with mostly manual means for generating negative pressure that drives infiltration. (But also wind, and pressure differentials caused by temperatures in winter)
In our case, we're definitely considering either an HRV or ERV to supply fresh outdoor air that we control (input and output CFM, MERV #). Our indoor air quality is poor enough to the point where we live with the tangible symptoms (Rhinitis), not just numbers on a sensor.
For those with interest in these topics, I suggest skimming a copy of one of the ASHRAE fundamentals handbooks[1]. It reads as a textbook but has incredible depth into the physical sciences that relate to building science, heating, cooling, and ventilation.
> In a modern home, there should be supply and return vents in every room.
That must vary by region. I live in the PNW, and I have not seen a recently built house with a return in each room. One or more supply vents per room depending on size, one return for each floor seems pretty much standard.
Interesting. I live in the upper midwest and remember my first home I lived in (parents built it new in 1980) had returns in every room. My current home is primarily forced air and there are returns in every room with multiples in the larger gathering spaces. Was built in the late 90s and I think building code may require a specific number of returns per square foot.
Could be regional -- I would bet that in most cases houses in the upper midwest have to deal with much colder temperatures in the winter than houses in the PNW. Maybe that influences the HVAC design.
But I wouldn't be the least bit surprised to find that there isn't really a specific reason, it's just "how we do things in this area." A surprising amount of building choices seem to be made that way.
Over here in Finland, nobody has returns in each room. It's a cold climate, so houses are heavily insulated, and moisture condensation is a concern during the winters.
We typically have returns in toilets, showers, etc. with one or more supply vents in each room; a large room may have several. Air flows in via supply vents, flows out under mandatory gaps in doors (if closed), through to the toilets and then outside. Moisture, CO2, and smells are constantly flushed in the right direction.
When the hood is on for cooking, air supply is typically enhanced so it doesn't mess up the overall pressure too much.
Incoming air is filtered, of course. The ventilation unit transfers heat from outgoing air to the incoming air to save energy and avoid problems with condensation.
In my home office, TVOC as measured by an Eve Room rarely goes above 100 (mostly happens when I pour an occasional whisky in the evening).
Old houses don't have ventilation machines at all, but rely on natural ventilation instead: warmer air flows upwards via chimneys and such due to gravity, pulling in fresh air from whatever gaps the structure has (accidental or purpose-built).
In the last decade I built 2 houses in the same neighborhood over 6 years. The first didn't require a return per room and the second one did - they had changed their code. A few years later and they had reversed their decision.
I guess the point is that it depends on when and where something was built. My most recent home is only a few years old and doesn't have a return per room and no code to say it should shouldn't.
A 1" door undercut is only about equivalent to a 6" duct in cross section and that size should max out at 120 ft^3/min with well installed duct. If you have more supply then there will be airflow issues in that room/house.
I could add the door cut back in, install return transfer grill, or look into adding a secondary heat recovery ventilator that acts independently of the primary HVAC system.