Partially true, however there is no line-item veto so cutting funding requires legislation.
The president has limited ability to impound money - refuse to spend it. He\she is limited by the Impoundment Control Act of 1974. It provides that the president may propose rescission of specific funds, but that rescission must be approved by both the House of Representatives and Senate within 45 days.
You would be amazed how fiscally ‘stovepiped’ the budgets of agencies are. Very little discretionary money, all the ‘stovepiping’ is mandated by the Congressional budget process. That’s why when there’s a ‘crisis’ there’s all these extra spending actions to ‘plus up’ agencies involved in the crisis. In many cases its why we are almost always caught with our ‘pants down’ when something happens. We then scramble to get the initiative by throwing money at it.
Moving agencies would only work if it required no to minimal funding to do so. Building, leasing facilities, paying for transportation of ‘office O&M’, breaking local support contracts & starting new ones at the new facility, moving of employees, upgrading new facility etc. would require legislation.
It’s all simple to say, hard to do even under the best conditions.
If we have a republican congress with a majority of MAGA candidates it could be done.