I think its important to remember the "trust fund" is a book keeping entry. It holds special treasury notes that were loans of excess Social Security taxes to the general fund. Now that Social Security benefits cost more than the taxes collected those loans are being repaid out of the general fund to pay for social security benefits. That money mostly comes from new loans in the form of regular treasury bonds. In short, the money the general fund used to owe to the "trust fund" is now owed to other investors.
So what happens when the book keeping entry says there is no more money left in the "trust fund". The general fund has already been borrowing money to pay off the trust fund bonds and can go right on borrowing to pay full social security benefits as promised. There are other solutions and it is very unlikely anyone will decide its a great idea to leave a bunch of elderly people unable to support themselves or pay their debts.
As I understand the problem with AI it is also fancy book keeping. Companies are "investing" in AI and AI is using the money to buy their products. If AI fails to generate income they lose not only their investment but their customer. With overcapacity and no capital, they stop buying from their suppliers and lay people off and reduce expenses. Their suppliers likewise now have excess capacity and fewer customers and follow suit. The laid off workers stop spending so other companies also start to cut back. And so forth.
If you have enough large companies all putting money into the same pot and the pot disappears the problem can be catastrophic. That is the fear. It has nothing to do with how "important" AI is.