Simply put, profit, although the historical reasons vary. All of these registries were begun for specific historical reasons, but now they've become a sort of tradition or national industry, and inertia keeps them going, as well as the economic benefits.
Many of these initial reasons could be viewed as for the benefit of specific larger countries that had a great deal of influence over these smaller countries, as in the case of Honduras and Liberia. However, open registries brought some benefits to smaller countries as well: besides money, they allow small countries to raise their international maritime profile. It's the shipping equivalent of free advertising.
So the historical reasons vary. For instance, at least one purpose of Panama's register was to help US businesses to avoid US laws, whereas Liberia's was originally to allow the US government to avoid international laws.
The first transfer of ships to Panama's register in 1922 involved two
US passenger ships wishing to serve alcohol to passengers during
Prohibition [Note: this does not appear to be the first instance of flags of convenience in Panama]. More followed as shipowners sought to avoid higher wages
and improved working conditions secured through US legislation.
After World War Two, Panama's registry grew more rapidly as US
shipowners sought to lower overheads while European ones switched
flags to avoid high tax rates.
As demand rose for open registration, other countries in the
developing world formed their own. The US used Liberia's registry to
build a fleet of neutral ships during the Cold War.
Whereas Honduras apparently started its open register at the demand of the US United Fruit Company:
Several years later the small country of Honduras also adopted an open
registry but this was largely at the urging of the United Fruit
Company, which operated banana carriers to the Central American nation
and these were among the few ships to make use of the relatively
One important point is that countries are not always "bullied" into open registries, as it were, but that they can be advantageous for those self-same countries. For instance, in the case of Panama, rather than being pressured by the US or US companies to create anonymous fleets, the first flags of convenience were used to subvert the law of Prohibition for the sake of profit and growing Panama's presence.
The very first ship to fly a Panamanian FOC was the Belen Quezada, a ship used to smuggle alchohol between Canada and the US. However, Spanish ships flying flags of convenience rapidly followed.
The history of the FOC is difficult to trace but most references point
to the Republic of Panama just after the end of World War I and a
three-masted motor schooner by the name of Belen Quezada that traded
along the west coast. With the opening of the Panama Canal in 1914
Panama found itself in a unique geographical position regarding world
maritime trade but had few merchant ships, or even merchant crews,
under its own flag. Therefore it decided it needed a flag without
restrictions concerning owners or crew nationality. By means of law No
63 of 1917 Panama made an amendment to its fiscal code to allow such a
registration of vessels in the coastal trades. On 20 August 1919 the
1,141-grt motor schooner Belen Quezada, which was trading between the
Pacific Coast and Caribbean ports, was enrolled under the Panamanian
Within months Spanish shipowner Sota Y Aznar, predecessor to Spain's
later Aznar Line, made overtures to the Panamanian government for the
transfer of several of its ocean-going steamers to the Panamanian
flag. This resulted in an Executive Decree dated 7 October, 1921 that
the Spanish ships could come under the flag of Panama by paying a
registration fee of $1 per net ton and an annual tax of 10 cents per
I suspect that currently, economic motivations for open flag registries dominate. It's an easy way for a small nation without a large fleet of its own to build an international presence, raise its profile, and make some money with relatively little effort. Taking Panama as a typical example, simply looking at registration fees the minimum fee is 500 USD and the maximum is $6500. Since Panama at one point recently had over 8,000 vessels, that's anywhere between $4 million and $52 million. That might seem relatively small (although for almost no effort, it's not bad), but if we look at the example calculation given on the website, we see their typical value given when all fees are taken into account, ignoring the new ship discount, is actually $12,000 a year after registration, or about $96 million total. There are likely some hidden fees that the government isn't going to be straightforward about on their website that could drive up the cost more.
Since Panama has a GDP of 60 billion USD, and raises 10% of its GDP in tax revenue, these shipping fees could add up to as much as 2% of their tax revenue, which is pretty respectable. But this doesn't account for other advantages that the register brings in, such as having a huge fleet raising Panama's profile without the government needing to spend a dime, or having ships that the government can use for outsourcing without needed to fund them.
What's more, a country like Panama might have to keep these prices relatively low, to compete with other FOC countries such as Liberia that have lower GDP per capita. Indeed, Liberia makes even more money from the registry: a full 6% of GDP, and seemingly with less effort needed than Panama.