Because the US government operates in a restricted fashion that is not analogous to the freedom that ordinary people have, in the US, government action requires authorization, hence the many opening lines "By the authority vested in me as President by the Constitution and the laws of the United States of America, including..." in executive orders. So the first action mandated is that the Sec'y of Homeland Security
shall take all appropriate action and allocate all legally available
resources to immediately construct, operate, control, or establish
contracts to construct, operate, or control facilities to detain
aliens at or near the land border with Mexico.
That means there has to be a legal path whereby resources are utilized for this project. Congressional appropriation is one path. In a few other cases, such as the Smithsonians, the laws creating the institutions not only authorized appropriations (by Congress), it also allows them through various other provisions to receive specimens, and they have the power "to receive money or other property by gift, bequest, or devise, and to hold and dispose of the same in promotion of the purposes thereof". They also have the power to "to make such disposal of any other moneys which have accrued, or shall hereafter accrue, as interest upon the Smithsonian fund, not herein appropriated, or not required for the purposes herein provided, as they shall deem best suited for the promotion of the purpose of the testator". Note that this only applies to funds not appropriated by Congress: this discretion required an act of Congress.
So in lieu of a law authorizing the receipt of donations from "the public", donations cannot be accepted. Congress has authorized a general power to receive donations to reduce the national debt under 31 U.S.C. 3113, but not to fund other projects, such as build a wall.