The caveat to the "wage price spiral" is that we live in a system that demands ever growing profits. Given that profits are the surplus that remains after wages are paid, this means we expect the portion of prices that goes towards wages to be reduced over time. This means profit growth requires either wage suppression (easy) or a higher output per employee (difficult). If wages go up instead of being suppressed, this adds to the existing market pressure to increase profits while also removing and in fact inverting one of the two major mechanisms to increase profits. According to traditional economical theory this means the only thing left to do is increase prices to at least maintain profit if not profit growth as well.

In other words, the reason the system demands higher prices if wages go up (while the worker demands higher wages if the prices go up because they literally need money to survive) is not simply that higher wages drive up production cost but that businesses also need to maintain and increase their profits, i.e. the surplus that remains after all stock is sold, all services are rendered and all costs are paid.

There is no way to change this within the system but concluding that this means the problem is unsolvable mistakenly assumes the system can not be modified or replaced with one that does not have this resource allocation problem. Such a change just wouldn't benefit those currently holding a disproportionate amount of resources and wealth as much as the rest of us so it's not likely to happen without sufficient external force (and even then only if that energy is not directed elsewhere).