Because their cost imposed by federal internal and external policies adopted under the Congress' Commerce Clause powers (including when they are caused by decisions not to exercise Commerce Clause powers -- a decision not to act within granted power is itself an use of the power), and because while certain cities may the poster children for the problem, quite often when regional industries are effect, its not just one city in one state, but a whole state (or several) that suffer substantial net negative effects.
The commercial policy that Congress pursues which results in these harms is usually done on the premise that it is ultimately the best on balance for the nation as a whole, and that the harms some areas experience are more the compensated by the benefits experienced elsewhere in the country. Which may be true, on balance, but if it is, then taxing those that benefit to provide support to those that are harmed should be able to remediate the damage to those harmed while still leaving those who benefit ahead.
Not exactly truthful. Most "free trade" recent agreements (past ~30 years or so) come with some sort of TAA support [1][2].
Why is it the federal government's responsibility to do these things? These are implied powers which the states have responsibility for. The Constitution does not reserve any of these for the federal government.
You can't ignore human ego, denial, and the power of convention. All one-industry towns wane when their one industry either falls or moves. People complain, panic, and some even try to move to find better luck elsewhere.
Ultimately, the largest anchor tends to be housing/property, which in the US tends to be paid for by long term debt. When a town loses its economic engine, demand to move there drops to near zero and the housing values fall underwater at the same time when people need to leave. I fail to see why the federal government should be on the hook for something like this. It would be subsidizing failure in a large way.
[1] https://en.wikipedia.org/wiki/Trade_Adjustment_Assistance
[2] https://www.doleta.gov/programs/factsht/nafta.cfm