There are a few things to parse out here. The first and possibly most relevant to your question is that there's really not much evidence that the Russian ship Dmitrii Donskoi, which is the "$100 billion ship," actually has any gold in it (or much gold). It was part of the Russian fleet that sortied from the Baltic against Japan in the Russo-Japanese war, and was damaged at the Battle of Tsushima and in subsequent actions. There's no particularly logical reason why it would have 14 percent of all the earth's gold bullion on it -- if the Russians wanted to send that to Vladivostok or some other Far East post, it would likely have traveled by rail.

Anyhow, to the related question -- Yes, warships did carry gold and precious cargo in the past. You're correct to think that the Spanish galleons transported gold and silver from the New World to other places -- silver particularly to China and Japan via Manila, and both silver and gold to Seville in Spain.

Now, as to "why" they would transport precious metals upon a galleon, the reason is that people are willing to kill for precious metals, and pirates and privateering ships would try to capture Spanish ships.

The Spanish authorities laid down regulations for transporting gold and silver back to the Old World after French privateers sacked Havana in the 1560s. Outgoing fleets would sail from Seville to trade on the Spanish Main, and rendezvous in Havana with ships from Veracruz carrying Asian goods before sailing back home. On the western side of the Mexican peninsula, trade between Manila and Acapulco took gold and silver to the Philippines and returned luxury goods the other way.

Transporting trade goods on a large, well-armed warship traveling in concert with other warships actually makes a lot of sense, especially in waters infested with pirates. Although the great convoy trade eventually died out by the 1790s, the Spanish still used frigates or other fast, well-armed ships to transport bullion. (The action of 5 October, 1804, which is fictionalized in the book Master and Commander, Post Captain, was a successful effort by the British to intercept treasure being carried by Spanish frigates.)

There's also the more mundane/prosaic answer that warships do also have to have cash on board, to purchase goods and supplies in foreign ports without an agent, for petty cash onboard, and for crew wages depending on the time period and how this works. Salvaging the ships' safes was a major part of the Pearl Harbor wreck recovery process.

I am rather sceptical about the reported quantity of gold on board this ship. There seems to be little reason for her to be carrying that much gold. To explain why, we can look at another warship sunk in the 20th Century carrying a fortune in Russian gold. In April 1942, the British cruiser Edinburgh (sister of HMS Belfast, now preserved in London), departed the Soviet port of Murmansk as part of the escort for convoy QP-11. On the 28th April, she was torpedoed twice by the German submarine U-456, heavily damaging her. As she was being towed back to Murmansk, she came under attack from three German destroyers. While she managed to sink one of them, a further torpedo hit did fatal damage; she was abandoned and scuttled by one of the accompanying destroyers. Edinburgh was carrying about 5.5 tons of gold, worth £1.5 million at the time, and about £150 million today. This bullion was part of the Soviet payments to the Western Allies for supplies shipped to the USSR during the war. Most of the bullion was recovered by a British expedition in 1981, and split with the Soviets.

So how does Edinburgh relate to the Dimitrii Donskoi, the ship that has been located? The Dimitrii Donskoi was sunk during the 1905 Russo-Japanese War. She was part of the Russian Baltic Fleet, which had been dispatched to the Far East following the loss of the Russian Pacific Fleet to Japanese mines, torpedoes and shells during the early stages of the war. Thanks to an incident in the North Sea where the Russians fired upon British trawlers on the Dogger Bank, the Russian fleet was forbidden to travel through the Suez Canal, and had to take the long way round to get to the Far East. Once they reached the waters off the Korean Peninsula, the fleet was attacked by Japanese forces as it tried to pass through the Straits of Tsushima. Much of the fleet was sunk; while Dimitrii Donskoi managed to survive, she was separated from the remainder of the fleet, and sunk by Japanese ships the following day. The Baltic Fleet would certainly have been carrying gold with it - the sailors of the fleet needed to be paid, and the fleet needed to be able to purchase coal and food during its journey. However, these were relatively cheap. If Edinburgh was carrying £150 million in gold as payment for hundreds of tanks and planes or thousands of tonnes of food, fuel and ammunition, then Dimitrii Donskoi would not need to carry just under a thousand times as much to pay for a few hundred tonnes of food or coal. It's also worth noting that carrying that much gold would take up a prohibitively large amount of space aboard Dimitrii Donskoi.