Why Didn't the Kohen Gadol's Wife Make Chulent for the Arei Miklat?

In a recent post, I made mention of something recorded in the Talmud, in the Mishna on Makkot 11a, that since, by Biblical law, accidental murderers were stuck in the city of refuge until the death the Kohen Gadol, ex-Kohen Gadol, or Mashuach Milchama, the mothers of these kohanim would provide those stuck in the city with food and clothing, so that they would not pray that their son, the Kohen Gadol, should die. (Rabbenu Chanenel's version of the Mishna quite possibly only specified clothing.)

In a comment, Ariella of Kallah Magazine repeated a question she'd heard -- how come it was the mothers, and not the wives, of the Kohanim Gedolim who did this? She suggested that this reflected on a deeper mother/son bond than a husband/wife bond, or else that the wife would be busy with children -- and welcomed suggestions.

My first inclination, which may well be the correct one, is that this is essentially a kasha on a maaseh. Nu, nu, they didn't, for whatever reason. To expand upon this, the Mishna is recording an historical event. Now, how is it that all these mothers of Kohanim Gedolim all thought of their own accord to do this? I strongly suspect that they did not. Rather, at some point, some mother of a Kohen Gadol thought to do this, for the reason specified. When the next Kohen in line was appointed to the office, that Kohen Gadol's mother heard of this custom and adopted it. And so this became an established custom, or minhag. Would a Kohen Gadol's wife adopt this as well? I would guess not, as this was more in the established realm of what the Kohen Gadol's mother would do. Had a Kohen Gadol's wife thought of this first, it is quite possible that it would be the wives rather than mothers who did this.

Other possibilities present themselves as well. As one example, the Kohen Gadol had to marry a betulah. This means virgin, but also in some contexts means young girl - technically, one under the age of 12, for technical reasons I won't get into here. This is a derasha which occurs in Yerushalmi Yevamot daf 9 - betula velo bogeret to marry the Kohen Gadol. This in addition to the requirement she be a virgin. If so, the Kohen Gadol's wife could be quite young for quite a number of years, and not really up to the challenge of feeding and clothing the residents of several cities. {Update: Though as Tal Benschar notes in a comment, there is a grandfather clause in place.}

Also, a variant of Ariella's second suggestion -- perhaps the Kohen Gadol wanted his wife to stay in proximity to him, not touring all over the country and spending her time feeding and clothing all those people.

Other suggestions welcome in the comments.

Update: Chaim of Divrei Chaim points out that Acharonim discuss the related question of why the Kohen himself did not provide. See here. I would give my same answer as above to this question -- historically, this was how the custom developed, and furthermore, for the Kohen Gadol's mother to do it shows her rachmanut, but for the Kohen Gadol himself to do it would be gauche.