Let me add some clarity to why Mixtes have long top and head tubes. Ot what would be the distance between the seat and head tube if there was a top tube. They are usually designed for upright sweptback handlebars. The kind used on most 3 speeds. One of those handlebar models is called "North Road". With drop handlebars, your hand position is way beyond the front of the stem. With upright bars your hands are positioned well behind the stem. That necessitates a longer "top tube" to compensate.
Using upright handlebars positions your body much more upright too requiring the stem to be higher as well. A longer head tube prevents a crazy amount of stem to be exposed. Everything looks much more proportional when a frame using upright bars has a longer head tube.
This is why a road frame designed for drop bars does not convert well to upright handlebars. The seat angle will be too steep, the top tube will be too short and the stem at it max height will still be too low. When I was designing our IGH Ukraine bikes with upright handlebars, I discovered these reasons.
It is possible of course that some Mixtes were designed for drop bars. That would mean a somewhat steeper seat angle and a shorter equivalent top tube distance but probably still a longer head tube because even with drop bars it is likely the rider will be somewhat more upright than when on a road bike designed for speed. The closer the seat height gets to the height of the handlebars, the higher the stem will naturally want to be placed with the result that a longer head tube is preferable. Bikes can look pretty ugly with stems sticking way out.