This is the crux of the problem as i understand it (from an ex-muslim) perspective
When Muhammed(or whoever), wrote the Quran, he wasnt thinking 4th dimensionally.
He each ayah of the quran was normally written to either develop a part of the faith or to deal with a situation that arose around Muhammads life,
however the situations that Muhammad was responding to in the Quran were not mentioned explicitly in the Quran.
Also over time Muhammad changed his mind several times during his life, which resulted in conflicting information appearing in the Quran.
After Muhammad's death, when future generations tried to read the Quran, they hit a few problems.
Some ayah contradicted each other
some ayah were written in such generic terms that they could mean several things.
Some ayah mentioned rules without giving context to the rules, so interpretation of the Quran became very difficult if not impossible.
To deal with these problems two different knowledge bases were created, then first was Hadith and the second was a methodology to read and understand the Quran.
With regards to Hadith, around 150 years after the time of the prophet some scholars started collecting Hadith, but when they did this, they found
literally hundreds of thousands of Hadith that contradicted each other and the Quran. So these scholars developed a methodology to categorise the Hadith.
The methodology that was developed checked for consistency of the Hadith with Quran, the trustworthiness of the narrator of the Hadith,
existence of similar Hadith from unrelated individuals etc
This process generated several volumes of books that are considered Sahih(authentic) Hadith, the most famous of which are: Bukhari, Muslim, Sunan Abu Dawud.
Without the support of these Hadith the Quran falls apart as an incomprehensible mess of generic sentences with no clear beginning, middle or end. Ive heard some scholars say, that without the Hadith, the Quran it just a book(i don't know how they manage to keep their faith with that statement).
So to answer your question, how important are Hadith, I would say that they are essential if you want to understand the main interpretation of Islam in existence today, i.e what you might consider mainstream Islam.
But when people say something like the problem is not the Quran, but the problem is Hadith, they are talking shit. One of the criteria of Hadith classification is that it cannot contradict anything in the Quran.
The Quran talks about most if not all difficult topics;
Slavery, Sexual Slavery, Sexual Slavery with Married Women,child marriage,beating wife,gods punishments, killing unbelievers.
The only thing that Hadith does is to provide context and embellishments to the core message.
Muslims cannot accept that any problems exist with the Quran, because they believe the Quran is the literal word of God, and admitting any moral problem with the Quran is tantamount to apostasy, so they will try to deflect attention somewhere/anywhere else. The most common deflections are:
The words of the Quran have been misunderstood, i.e words have been mistranslated, or context has not been understood correctly.
The true meaning of the Quran is only known by Allah.
The Hadith are fabricated, or weak so cannot be trusted. And when they are shown Hadith from a Sahih(authentic) source, they say the Hadith was incorrectly classified as Sahih, but is infact weak.
people abused the word of God for their own evil intentions, its not what god intended.
Hope that helps