There seems to be a sad pattern when reading the history of WW1-WW2 ships, they played such a historic role, but those that survived were all sold for scrap.
- HMS Dreadnought - first of her kind
- HMS Warspite - fought at Jutland and through the Second World War.
- All of the battleships
If we specifically look at HMS Dreadnought were they simply motivated by money or were they not interested in the preservation of these kind of ships, were they seen as uninteresting, was there no public outcry?
There are several reasons why ships that might be seen as historic were scrapped. It should be remembered that the RN has never operated museum ships itself. Britain's museum warships were sold by the RN to the organisations that now operate them, much as those that were scrapped were sold to scrapping companies. As such, the question is as much 'why did no organisation decide to purchase these ships?'
Probably the most important were doubts that museum ships would be profitable. It cost a lot of money to restore ships and make them suitable for museum service. The restoration of HMS Victory cost ~ £160,000 in 1922, equivalent to ~£10,000,000 today. To this must be added the ongoing maintenance costs. Ships require a lot of maintenance, spending a lot of time in salt water which corrodes their hulls; to this must be added costs for keeping machinery in good condition, paying staff and the like. As a result, there was considerable scepticism about museum ships in the early-mid 20th Century Royal Navy. It was felt that ships with undistinguished war records would not draw sufficient visitors to pay off their ongoing costs. Victory, despite being one of the (if not the) most famous ships in the Royal Navy's history, struggled to raise public money to pay for her restoration. Turning Dreadnought, a ship which, despite her technical pre-eminence, had done little in WWI, into a museum ship was considered unlikely to turn a profit. Warspite had been heavily damaged by a glide-bomb and then by a mine; repairing her would require far more funds than any organisation would be willing to spend.
Scrap metal was also important to the British economy. Let's look at the British ship-breaking industry following WWII. This was handled by a government body called the British Iron & Steel Corporation (Salvage) Ltd or BISCO, which also handled the supply of other raw materials to the steel industry. Ships the Admiralty no longer needed were handed over to BISCO. BISCO would then assign the ship to a suitable breaker's yard, where the ship would be scrapped. Following this, the scrap would be sold, the costs of the demolition returned to the breaker and the remainder of the money returned to the Government. This brought in a lot of money- in 1945 pounds, scrapping a battleship would bring in £450,000, while scrapping a destroyer would bring in £30,000 ($26,000,000 and $2,000,000 respectively today). You also need to factor in the reduced costs to the Admiralty, as there was no longer a need to man or maintain the scrapped ship. This also produced a lot of scrap. Annual output from the British ship-breaking industry was about 500,000 tons, or about 3% of the output of the British steel industry. For a nation like Britain, whose industry had been devastated by the war, and which owed the US and Canada £3.8 billion (again in 1945 pounds), this was an attractive option to increase revenue and rebuild their industry.
It's worth noting that Victory was the only Royal Navy ship to be preserved before the 1970s. While ships from before that decade do survive, they had often spent years in mothballs or serving in subsidiary roles. HMS Warrior, the world's first iron-hulled warship, spent much of the 20th Century as a depot ship and oil jetty. The WWI-era monitor M33 had been a training ship, depot ship and floating offices in the years after WWI. The old sailing frigate Trincomalee had been sold to an entrepreneur for use as a sailing holiday camp. There was comparatively little interest in preserving Britain's naval heritage for much of the 20th Century.
Cost. The same sort of discussion is happening with the USS Texas, today. Keeping a warship afloat is not an inexpensive affair - they must be maintained, from simple things like keeping their exposed surfaces polished and painted to prevent rust, to major concerns like maintenance of pumps and ventilation systems.
In some instances, there is sufficient national pride attached to a vessel that it sees enough tourism to pay for that cost.
This does happen less often with ships that are "merely" jumps in technology, though - as, after all, the jump that made them so impressive at the time will naturally have been exceeded many times over by the time they are being evaluated for preservation. And particularly in that period of rapid naval advancement (and naval arms races), keeping now-obsolete ships in their entirety meant less could be done to keep the rest of the navy cutting-edge, thus many times the ships would be negotiated away in treaties outright (IE., HMS Dreadnought herself identified for scrapping as part of the Washington Naval Treaty).
Of course, even in cases where ships ARE sold for scrap, often enough, some artifact of the ship is still retained in a museum. For instance, a gun tompion from HMS Dreadnought still exists. In Portland, Oregon, there is the mast from the pre-dreadnought battleship USS Oregon. etc