Yep, when the party paying can decide not to pay and there are no teeth to extract payment, that gives immense power to the payer.

At least in my area, there are legal avenues if alimony goes unpaid. Assets can be seized to pay off late payments and wages can be garnished.

Its a different story if the payer truly can't afford to pay the alimony, but at that point they wouldn't have the immense power you are concerned with.