No support. The system has worked just fine like this so far, and I think the staff intended it this way. Lionesses are only needed for the game function of breeding and hunting, so unless it is pregnant you have it available to hunt 24/7. It takes half an hour to hunt which means that (theoretically, with alarms) you can hunt about 48 times a day (Without replenishing hunts [since each lioness gets 10] this would take 5 sets of lionesses. If you use 3 that's 15 lions, if you use 5 that's 25.). At lower levels there is more a chance to fail, but once you get up higher, 3 lionesses can bring back 1-2 5 uses carcasses. With the theoretical 48 hunts that is 120-240 food uses per day (and it takes about 3 days for lions to get "I'm leaving" hungry, so in that time you would amass enough for about 360-720. Far more than anyone obviously needs).

Another thing is the stats. This would blow them up. Egg yolks have already been nerfed, so it is clear that staff are trying to get the stat market under control. Sending out all your lionesses would mean you can gain all of them their stats in no time. You also mentioned training adols, this would ensure that you could easily get all your adols to 100% which gives a stat boost (Oh look more stats). This suggestion would likely blow up the stats gained by females greatly, something we don't need. It's regulated well enough currently.

You also have to consider the food market. This suggestion would likely ruin it (Farther, since food goes for 500-1200sb/1gb for 100 uses despite being 50 uses for 1Gb in the oasis). You mentioned that they would all bring back their own kills, so if you send out 3-5 in each party and then all bring back 1-2 5 use carcasses a single hunt would give you (with 4 hunting parties) 20-40 uses. This doesn't even account for prides that could afford to send out nearly 10 parties. [Also I assure you I'm not pulling statistics out of my ass. My numbers are based on real things my hunters accomplish daily.]
So, following what I said earlier, it would be very easy now for everyone to obtain 100 uses (with the earlier mentioned statistics it would take about 3-5 hunts. With 24/7 numbers that's 480-960 uses per day, 1,440-2,880 by feeding day [Day 3]), and so there would be an influx in unused food and the market for it would drop drastically because it would be so much easier to obtain.

I think how the hunting system currently works is important to learning balance. You have to balance how many pride members you have with how often you can hunt to provide for them and how much you think its worth to shell out currency in the event that you cannot obtain all the food you need. Most people that have 50+ lions work hard to hunt for them, and in the event that they cannot find all the food they buy it. Sounds harsh, but if you cannot feed all of your pride it might be time to thin the ranks (especially those naughty hunters bringing back a useless human leg every time, shame on them).