Actually the hells are there for specific types of sins. Sin in Hinduism is not a concept. Adharma, however, is. Adharma is categorized into many subclasses. I will give a few examples to highlight the existence of such special classes of hells.
"A man who kills a cow, foetus, or indulges in arson, descends into
Rodha. A killer of Brahmanas fall into Shukara, and so a drunkard, a
gold thief, a killer of Kshatriya or Vaishya fall into Taala".
"He who kills a Brahmana or defiles his teacher's bed, or has sexual union with his sister falls in Taptakumbha. So also a soldier who
speaks lies". (3.57)
"Similarly he who sells liquor and he who discards a devotee, also falls there". (3.58)
"All these fall into Rudhirandha. Those who administer poison into their guests sitting in a row, fall into the fierce hell Vidbhuj.
There is no doubt in this". (3.68)
So this is just an example of why there are special hells. A sinner usually passes his time for specific Adharmas committed and the rebirth is usually for Adharmas of small measure. There are many many more verses you can look up in Garuda Purana's Dharma Kanda.
Your main answer can be summed up in a few verses from Garuda Purana only.
Part 2: Dharma Kanda
"The sinner is born again and again and dies again and again till he
has exhausted his sin and acquired virtue".(3.84)
Shri Krishna said, "Whatever sin a man commits consciously or unconsciously stands in need of purification by means of atonement".
"Whatever gifts a man has given, all stand in his favour at the hour of death". (4.16)
"If he accepts sannyasa as prescribed in the sacred texts, he is not reborn but is merged into Brahma". (4.37)
I know this doesn't answer your question 100%, but at least you get an idea of the hell. Its not a Christian hell, wherein any sin you commit, you end up in a fiery place. No, Sanatan Dharma has specifics. You won't even stay in a hell for even a second more, after you've finished your punishment quota. That's the beauty. Its all about Chitta Shuddhi.
~ Special thanks to @TheDestroyer for providing me with the Scriptures.