It's because they are cheap rifles to buy and cheap ammunition that's why people used the 30/30.Definitely not because it's the best choice.
I guess it's all about what you mean by 'best'.
No doubt there are more powerful rifles, ones with more foot-pounds of energy, ones capable of stopping a charging bandersnatch in its tracks.
The .30/30 kills deer reliably. It does so with current modern loads with expanding bullets and smokeless powder. It did so with cast bullets and black powder.
Dead is dead. Will those extra foot-pounds you are paying for kill Bambi any deader?
There are certainly more accurate rifles, ones able to take down a deer at 600 yards.
At the OP's stated maximum range of 50 yards, the cheap, lightweight .30/30 can put a round into the boiler-room ten times out of ten - the famed 'minute of Bambi'.
How will a more expensive rifle, with its more expensive ammo and more expensive sights, do any better? Can it hit the target eleven times out of ten?
How will the additional weight, recoil and expense make your choice better than something that is perfectly adequate for the job?
Will it carry itself?
Do the skinning?
Carry out the gutted animal?
Sing you songs and massage your feet?
Of course not. Just as there are men who think they can make their willies longer by buying a Lamborghini, there are hunters who feel that anyone not carrying the newest .397 Megamag Shoulderblaster is hideously undergunned and shouldn't even be in the woods, let alone seriously hunting.
The simple reality is that the .30/30 (despite its shamefully low cost) does
everything required of it in the situation the OP describes. Low recoil, perfectly adequate accuracy, perfectly sufficient power and light weight. If one can bring oneself to overlook the horrible shame of not carrying a rifle worth three mortgage payments, I think it's ideal for the job described.