Laissez faire was always going to be a light touch government policy.
British government was far less of an all encompassing entity in the 1840s than it is today or even compared to the reach of government by the end of the 19th century.
Great Britain and Ireland were administered in the 1840s by local grantees for the most part. Magistrates, poor law boards, landowners, and local lord lieutenants all wielded local power. In Ireland, military occupation was the means by which the island was kept quiet. Suffrage was severely restricted in both Great Britain and Ireland, and MPs represented only very limited constituency interests. Tithes were owed by all to the established church on both islands.
The task of dealing with the crisis caused by the Famine was left to the poor law unions. Poor law unions also existed and operated in Britain. The poor law unions ran the British workhouses Dickens described, and there were also workhouses in Ireland (many were later converted into county hospitals). Local taxes supported the workhouses.
It simply didn't occur to politicians or government/ mandarins ( or anyone else) that national government should play an immediate role in the lives of the people. The role of the national government was not imagined in that way until the next century.
Thst being said, Trevelyan's attitude tipped into support for the idea that land should be managed with only profit in mind, and the calamity of famine presented an opportunity to reorganize or rationalise land management. And Trevelyan had a great deal of impact on the course of the Famine.
Your statement is a bit of a straw man - only the very poor were to be allowed to starve or cleared off land that would be more profitable if turned to grazing. Land clearance had been embraced previously during the Highland clearances. It wasn't a moral problem for those landowners who decided to charter ships and drive families off their lands or simply whistle up the militia and have them thrown out on the roads. Nobody at any point contemplated the death of all the Irish.