Why aren't the bottom of plane fuselages flat?

Why are almost all jet airplane fuselages perfect circles? Wouldn’t flat bottoms reduce drag by reducing area and create a lifting surface? All else equal, couldn’t a plane with a flat bottom fuselage get better performance?

I know there are consideration like connecting the pilot controls to the steering surfaces and the idea that a cylinder is the easiest shape to pressurize, but assume the plane is fly-by-wire and doesn’t need a physical connection to the cockpit, assume its construction is strong enough to pressurize whatever shape, assume that there is still adequate room for baggage and fuel, etc.

Basically would a fuselage with a flat bottom be more or less aerodynamically efficient then a circular fuselage cross-section assuming that the fuselage has the same cross section area.

For a given area, a circle has the lowest perimeter, so from that point of view, you should get more drag with anything other than a circle.

For what you really want to know, maybe you should instead consider the area you lose by flattening the bottom to be wasted space anyway, so that your perimeter actually gets smaller.

That and also that if a flat bottom would produce lift, you would need less wing and could reduce drag from that, no?

The bottoms of quite a number of large aircraft are flat. Around the wing box (where the wings attach to the fuselage) the bottom is almost always flat - in fact, I can’t think of a commercial aircraft that doesn’t have a flat bottom.

Some photos:

Boeing 737 underside
Airbus A320 (its flat beneath the wing fairings)
Airbus A340 underside (youtube video)

The fuselage in front of and behind the wing box are indeed round, for the reasons you already said, but the middle is very much flat.

A flat-bottomed fuselage, even if airfoil shaped, amounts to a very short span wing. The part of the wing near the tips is inefecient and draggy due to air spilling from the high pressure underside into the low pressure top side. A short span wing is essentially all tips.
The best solution is the cleanest, smallest fuselage that will get the job done, carried by the longest, narrowest wing you can build strong enough.
Think of a high performance sailplane.

A fuselage (of an airliner) is a pressure vessel, and a cylinder is the best shape for the purpose. Fairings flatten out some areas, but their purpose is to reduce drag at such places as the wing/fuselage intersection where a sharp angle is not desirable.

Putting a flat bottom on the fuselage would not make it a lifting surface. Lift comes primarily from the angle of attack of the wing, and even to the extent that shape is relevant at all, it’s only the side-view cross sections that matter.

Other than making it a cylinder, how do you make the construction stronger? Presumably by adding struts, braces, etc. on the inside, or by making the parts you already have thicker. But that adds weight, which decreases the performance of the plane. The lightest way to make the plane strong is to make it a cylinder, and in aviation, weight is money.

What if the plane had chines as in the SR-71? Supposedly they added the chines the the fuselage for stealth purposes and then were extremely surprised by the amount of lift they added, allowing them to keep the chines (they were originally skeptical that they would work at all) and decrease the size of the wing.

Is there any discussion of chines in planes that don’t need to be stealth?

Expense to produce and overall size. $$$$$ rules. It is always a cost / benefit ratio type decision.