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Some higher end homes have a make up air system for venting a stove top in air tight houses, but it is so expensive.

Are you describing something different than the overhead fan equipped above the gas range in most new homes?

They are describing a system that automatically creates a path for replacement air when the overhead extractor fan turns on, which is also achievable by opening a window.

Absent replacement air, stove extractor fans (like any extractor fans) cause an airtight house to experience negative pressure and reduce the effectiveness of the fans.

I believe you are referring to a Heat or Energy Recovery Ventilator (HRV or ERV). In the absence of a range hood they would be better than nothing. But they aren't designed for the large volume of air changes that cooking requires.

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