It's based on a number of factors, not just financial.
Yes, optimum yield for time and labour input is one of them. We all know muntjac are very tasty deer, but the amount of fiddling about required for such a small amount of meat is barely justified. At the other end of the scale are reds, which will of course yield more meat, but are big things to move about and might require equipment (hoist, etc) beyond what a domestic kitchen has. And there's extra work on a red to take the cuts down to a size that the average small family might want to use. Every time you pick up your knife it adds to the "cost", whether real or hypothetical.
So really, that leaves 3 species in the running for "most economical": roe, sika and fallow.
Sika can be discounted straight away as they're not everywhere, and if a lot of travelling is involved in filling the freezer it's not economical at all.
And then there's quality. You need quality if you want repeat customers (or in this case, if you want your family to keep on eating it). I spoke with a number of chefs and restaurant owners, some of whom were themselves stalkers, and without exception the only venison they wanted to put on their menu was fallow. It gave them the best balance of ease of handling, size of cuts, eating quality and cost. They definitely did not want red: "too coarse, and too similar in texture to beef. Quality not consistent" was the general consensus. Roe was considered to be of excellent eating quality, but a bit on the small side to be really cost effective, and excessive % waste from shot damage.
As for it being best from a pricket or young doe, that's the ones that not only give the best eating quality, but also the least amount of waste during butchering, and in order to be economical waste must be minimised.
(I haven't mentioned CWD in this appraisal, because they taste nasty

).
Incidentally, I think your figures are a little bit out. A 30kg (larder weight) fallow pricket or young doe will yield close to 20kg of saleable lean meat, with a retail value in the region of £350
They are a very economical carcass to work with, in so many respects. And there's lots of them.