The way this question framed, it is basically that Rashi says X, I think not X, so what is Rashi's logic. It may simply be that Rashi doesn't agree with your premise. (I am writing this not to be rude but because it seems like a common trend in the questions you pose, and this, by itself, might be the overarching answer.)
To the specifics. Firstly, Rashi begins by explicitly crediting Bereishit Rabba for the basic idea, although Rashi does expand upon it. Rashi fleshes out details and mentions animal work, parallel to human work. Bereishit Rabba states the following, and credits Rabbi Elazar with the idea:
וילן שם בלילה ההוא ויקח מן הבא בידו מנחה לעשו אחיו עזים מאתים ותישים עשרים
אמר רבי אלעזר:
מכאן לעונה האמורה בתורה, הטיילים בכל יום, הפועלים שתים בשבת, הספנין אחת לששה חדשים.
שהן צריכות תיישים עשרים.
שהן צריכות אילים עשרים.
ובניהם שלושים ובנאיהם שלושים.
The idea is that the onah, required marital relations, differing for different human tradesmen, is here derived, or alluded to, in the Torah, from Yaakov's actions. How so, because we see that in Yaakov's gifts, he gave a different amount of males per female, because, from a practical - rather than halachic - perspective, this is the amount a breeder would match up, because of differing practical needs of the species.
This does not mean that there is a halachic requirement of onah by animals, as you are assuming. And I don't think Rashi or Rabbi Eleazar said otherwise.
IMHO, if only one mating is needed to impregnate a female, one male is sufficient for any number of females, given enough time
Yaakov was an extremely successful breeder, as we saw in the previous sidra regarding Lavan's sheep. Being a successful businessman, and multiplying your wealth, requires that you breed your animals in the most efficient manner possible, not to take one male animal to impregnate your sheep over several decades. In Vayeitzei, he worked with the striped rods not because of a sense of halachic obligation of onah for the poor female sheep, but to build wealth. So too here, the appropriate gift to Esav would be a sustainable one in which wealth could be built. That is pshat in Midrash Rabba and in Rashi, not what you are presuming and then asking about.
You further ask:
Also, I don't know of any empirical support that working animals (bulls) have lesser mating patterns than non-working (rams).
I don't know either, but this was presumably either the direct observation of Rabbi Eleazar or the assumption made based on a plain reading of the pesukim. Chazal often derive facts about nature from pesukim rather than citing scientific studies. They even have proofs from pesukim that the sun rises in the east and sets in the west, and of the direction from Eretz Yisrael to Bavel.
That you haven't seen empirical evidence to support this idea - well, firstly, have you seen empirical evidence that contradicts this idea? Without that empirical evidence, it isn't much of a question on Rashi. And even if such contrary empirical evidence exists, why would you assume that Rashi would be aware of said evidence, such that he would need to explain his logic? Perhaps he relied on the science stated by Chazal in Midrash Rabba, which he is surely entitled to do!