I do not think that the tailplane needs to create downforce to provide stability in normal flight. After all, the main wing is not unloaded in normal flight.
Consider for simplification a plane where the stall AoA of main wing and tailplane are precisely equal. However, they are located at different angles to fuselage and airflow.
How does tailplane stabilize the plane? Well, suppose that the nose pitches up so that the main wing AoA exceeds stall AoA and main wing stalls. It does still produce some lift, but less than before.
If the AoA of tailplane is smaller than the main wing AoA then the tailplane has not yet reached its stall AoA and generates lots of lift. The main wing drops but the unstalled, lift-generating tailplane turns tail up so that main wing AoA decreases below stall AoA and the wing resumes flying.
If tailplane had same AoA as main wing, they would stall simultaneously. And if tailplane AoA were bigger, the tail would stall first, turning the main wing to stall and causing deep stall.
Note: you do not need the tailplane to generate downforce when the main wing stalls. You could perfectly well use a tailplane that stalls slightly after main wing and which at the main wing stall is creating a lot of lift. All you need is that the tailplane AoA should be smaller.
The other limit is at forward CoG limit. If the tailplane reaches inverted stall negative AoA, the plane falls over.
Some planes are deliberately unstable in pitch. Such as Wright Flyer, and this is pilot flown like several other unstable planes. There are also unstable planes flown by computers.
Assuming you want some definite amount of positive pitch stability, there are several ways to reach it. Such as having a small tailplane which produces downforce most time and is close to inverted stall at forward CoG, low AoA condition. In which case you are going to have a large induced drag at the tailplane, plus the main wing must compensate the downforce with extra lift and suffer its own share of extra induced drag. Alternatively, you might have a big tailplane which is safely far away from inverted stall, have a AoA which is definitely smaller than that of main wing but close to it, and which produces little downforce or actually upforce, so that the induced drag at the tailplane is small, and the induced drag at main wing may be decreased. There would still be some trim drag - trim drag only vanishes when tailplane flies at exact same best L/D AoA as main wing and at that condition stability also vanishes. But when do you minimize the total trim drag for a given amount of stability?