Why did Bronn get this position?

Question

Why is Bronn

Master of Coin?

I understand he became a Lord since Tyrion promised that to him, but he was never promised the role of

Master of Coin or a seat on the Small Council.

In fact, he has no apparent skills that suggest he's good at that particular job because

Tyrion once had to explain loans to him.

Additionally, he's not a particularly serious person, he's politically inexperienced, and perhaps most importantly he is morally dubious. It just seems to make no sense from all perspectives, so why was he awarded such an important position?

Answer 1

Probably because he is Lord of Highgarden

We know that the Tyrell's were the richest House in Westeros once the Lannister gold mines ran out.

Tywin: Our last working mine ran dry three years ago.
_{Game of Thrones - S04E05: First of His Name}

Highgarden is connected by highway to the three largest cities in Westeros (King's Landing, Oldtown, and Lannisport). The Reach (of which Highgarden is the capital) has the biggest economy, is the most populous region, and is one of the major breadbasket regions of the Seven Kingdoms (along with the Riverlands).

As the most fertile region of the Seven Kingdoms, we grow the lion's share of the grains and fruit that feed this country.
_{Margaery Tyrell in Game of Throne's Season 3 Histories & Lore}

So between the income from feeding the rest of the kingdom and taxing everyone who lives in The Reach, Highgarden has a massive and continuous, source of income.

With this in mind, it stands to reason that Bronn is now probably the single most wealthy man in Westeros, and as such to be Master of Coin is a small leap.

Answer 2

The people placed on the Council under the reign of Bran were people that viewers were already familiar with, were allied with Tyrion, Jon, or the Starks, and could at least somewhat fulfil that role.

Bronn was no stranger to viewers, and was for the most part an ally to Tyrion.

Bronn, whilst not explicitly showing any finance skill in the show, had been associated with money/coins throughout the show. He was a sellsword; it was his nature to do things for payment. And through his service, he rose from a simple sellsword to Lord of Highgarden, greatly increasing his own finance. One of the key reasons, if not the key reason, why Littlefinger became Master of Coin in the first place was that when he was customs officer at Gulltown, he increased revenues tenfold. Bronn had increased his own finance by far more than what Littlefinger did to get the position, demonstrating his strong ability to earn revenue (alas without traditional financing skills). Given his strong association with money and how much he's gained, he would be somewhat able to fulfil the role of Master of Coin.