The argument works, but is too simplistic as other comments mention, and only looks at an ideal-state.
It's unfortunate that politicians are often responsible for making this decision, because most of the time they fail to understand the economics, and make decisions that optimise their term in office or other selfish interests.
I live in South Africa. Last week the governing party made a resolution to "look into" UBI/basic grants. [0]
Today, thousands of disabled and old people were queuing for their basic grants, in inhumane ways, during a pandemic + a South African virus variant that's more aggressive. The Minister in charge of social development, said "there's no money" [1].
Revisiting the engineering argument. It talks about fail-safes if the elevator stops working. This partly assumes that the elevator is maintained, because it not plunging is less of a concern than it being stuck for weeks at a time. If governments fulfilled their social duties, the overall cost of living would remain low, those in need of social services would regularly get them (without the strong need to pay people money). This reduces the bang-bang effect mentioned.
Productive labour forces also minimise the length of elevator failures.
If we look at Maslow's Hierarchy of Needs, with a view of universally solving them; we'd be incentivised to optimise for food production (reduce hunger), providing basic + better shelter (reduce homelessness).
Play fair with resources to improve safety (colonialisation, domination, creating wars, displacing people, increasing crime).
Doing a lot of these things, and addressing the ills of capitalism, become the fail-safes that diminish the preconditions that allow people to argue for basic income (where the recipient is an able-body who is not being productive by choice or circumstance).
[0] https://businesstech.co.za/news/finance/459738/government-to...
[1] https://www.news24.com/news24/southafrica/news/auntie-theres...