An analogous situation to Hunter being on the board of Burisma would be the people on the board of Theranos. If you remember, Theranos was creating a new way of doing blood tests and they raised hundreds of millions of dollars. However, their technology didn't work and they hid the failures from everyone. The board had a lot of top military and political people, such as Henry Kissinger, James Mattis, and George Shultz among others. None of the people like that had any experience in developing medical testing equipment. They were likely hired for the board for other reasons, like their contacts, their advice on business, their ability to organize and execute, etc.
Trump holding back aid to Ukraine until they investigated Biden+Burisma would be like S. Korea holding back military compensation payments to the US until they investigated Mattis+Theranos. Even if those companies are corrupt, they are essentially unrelated to the money being held back. And just because a big name is on the board doesn't mean they got there because of corrupt reasons.
That is not a good analogy. None of the people you mentioned involved with Theranos had close family members in decision making positions in government. None of them had a child, parent, or spouse in Congress passing laws affecting Theranos. None of them had a child, parent, or spouse at the CDC making approval decisions. Thus, there was no conflict of interest
Yes, those people had connections and they had name recognition. But that is different than conflict of interest within government.
If Ukraine was investigating Burisma while Hunter Biden was a highly paid board member, there was the possibility Hunter stood to lose out on millions of dollars, and, potentially be found guilty of a Ukrainian crime. Whether or not Hunter actually violated any Ukrainian laws was irrelevant, there was the possibility the investigation could result in at least significant loss of $$ to the Biden family.
So, enter Vice President Joe Biden. He withholds official US funds from Ukraine unless they immediately (within 6 hours) fire the prosecutor. Vice President Biden was operating in his official US government capacity as Vice President and as the person assigned as point duty by President Obama.
So now the question becomes why Joe did this? Was he thinking about his son's position? Was he thinking about the millions of dollars his son was being paid? Was he concerned of the possibility of a criminal charge against his son? Aren't those things all possible
? Mightn't a rational adult conclude there appears to be a conflict of interest?
Now, Trump asking for investigations from Ukraine does not enrich him or his family. You are arguing he had a conflict of interest because Joe Biden might become the Democratic nominee in the 2020 election. So, your argument would be that anyone who is of the opposition party should not be investigated even when there is ample evidence of possible corruption. Except, of course, when the Dems were investigating Trump for Russian Collusion. Because, ???