"In short, if you want to incentivise people to work, you need to pay them more."
The extra you pay them will be a subsidy. Because if what they are capable of doing were worth more, they would already be offered it. Ultimately all subsidies are paid by the productive part of the population. There is no "free money" that magically appears because you attach the initial burden of this subsidy to employers.
As a matter of policy it seems to currently be a popular idea that everyone who is not independently wealth should work. We already accept the idea that some people only partly pay their way, by working and claiming tax credits. We just need to extend the number of available jobs so everyone can do this.
Imagine if everyone on benefits was willing to work for free. Do whatever they are capable of, for nothing at all. Surely 95% of them are capable of doing something useful? For example clearning/childcare/gardening for neighbours who can't afford to pay for this at the current minimum wage.
Now imagine that minimum wage is reduced and UC is changed so that there are no out-of-work benefits for able-bodied people, but people can still achieve today's level of incomes from working plus tax credits. (Tax credits would be costing more of course, taking up the slack from lower wages.) Suddenly everyone is willing to do any work, for free, or as close to free as the minimum wage allows.
From an employer point of view, people would be working for as close to free as is necessary to ensure everyone can work. (Note it is the workers who are being subsidised, not the employers, who are only paying what the labour is worth to them.)
From a benefits system point of view, the money paid out is money that would mostly have gone out in benefits anyway, so it may not be a huge extra cost. What extra cost there is is the subsidy we are willing to pay to achieve the public policy objective of having everyone in work. It will come from taxes, which is a fairer source than the random selection of people who will suffer if one had merely increased wages. (That solution might ensure some people were paid more, but would probably destroy rather than create jobs.)
The minimum wage should become location specific and tied to the local unemployment rate, so that the state of the local economy at a particular point in time would determine the extent to which the benefits system was subsidising workers there. It should fluctuate at least annually with the state of the local jobs market.