Well i suppose its because we're people, and most people won't ignore another creature, no matter how small or insignificant, when in great distress if we can help it.
I want to say more on this subject though than just that, if i may.
Wether we help the root cause of the issue that made the creature suffer is another matter and highly controversal topic. I don't think theres anything wrong in saving individual bettas, its even admirable at times i believe, but i refuse to buy lots of sick and dying bettas myself from lfs's as i wouldnt want to,
a. End up in the situation where i have so many i can no longer look after them or my other fish to my best ability, or
b. Buy a dying betta from a lfs only to pay for more in its place.
I see alot of sick and dying bettas a lfs i sometimes go to, but i generally ignore them and just preach to the staff a bit about keeping them instead- i not insensitive or an ogre, and i do care a huge amount about fish, but theres little you can do about bad petshop bettas apart from educate people about them.
Theres nothing wrong with taking unhealthy bettas off friends or people you know in general, and its even better if you know for sure they are not going to buy a replacement fish in its place that will suffer a similar unhappy fate, and/or that you tell the other person where they went wrong with the last betta

.
In my honest opinion though, if you are just saving a petshop betta because its not well cared for, and you don't tell anyone about keeping the fish properly there and then however you do it, and you take that betta home...I honestly don't think theres anything wrong with that, but you must take into consideration that the money you gave for that betta will only pay for more who will suffer a similar fate, and that them creates little point in saving th single fish if you are concerned about other bettas in the same situation.
Most people don't think about this when they buy bettas though...I know plenty of
excellant and knowlegable betta keepers here, who have done just this, and i am sure they didn't buy that dying betta because they wanted more in its place to suffer the fate it shared before they bought it, but because they cannot stand the thought of it just dying there before anything can be done, and that their heart wont let them leave it there to do this, because well, they are people with good hearts...
There is also great reward in getting sick bettas back to good health, and when you have done this you have made a big difference to that betta. But only that betta(if that makes sense, not that makes it any less important though).
I only have one betta myself, a male VT betta who was a rescue case(starving and had septicemia). I did pay money for him and i did try to educate the staff at the lfs. I think though...He will be the only betta i will be getting for now, until the day he dies. I bought him because i already wanted a betta before i saw him, and i guess i thought i might as well rescue him since he came from such an unreliable lfs- the guy who i talked to about keeping bettas, was very grateful for the info i gave him, he said that he hated seeing the bettas die all the time but before i told him the info on caring for them, he just didn't know what to do.
So i guess we all came off a bit better that day

.
Anyhoo, thats just my story and opinions, Good Luck with your new bettas Mis Dib Dabs and hope they recover to full health

.