Because more in wages ultimately = more tax.
The jump in the NMW in April will increase Tax revenue, as more people will find themselves over the thresholds, and start paying it, and those already paying it will pay more. The same raise will cut the benefits bill by meaning more people earn more of their income rather than claiming it.
Beyond that, VAT, PAYE, NI Contributions, (and pensions contributions but they don't help balance the books now, just eventually) Corp tax etc etc are all percentage taxes.
This means that more in wages means more in contributions from businesses. In turn, they put up prices, increasing VAT and (possibly) Corporation Tax takes.
People with more money in their pockets spend it in shops and restaurants and service businesses, putting money into the economy to keep it buoyant. Of course, that's also more tax running through the government coffers and keeping the country liquid. They buy property - stamp duty and eventual inheritance tax. They invest - capital gains tax.
There's also the issue that, in some cases, they really have no choice. You can't hike the NMW by 9.7% this year, on top of around 7% last year, on top of, on top of etc and not eventually expect the middle bracket to kick off and demand they're paid their value of their skills.
From April, the NMW balances out for a full time worker to around £20k a year before tax. That's any adult, doing any job for 37.5 hours a week.
Want people to spend years at college and then Uni training, at their own expense, and then do stressful, demanding, absolutely essential jobs? Pay them.
Want them to take on roles where they're responsible for the safety of others, sometimes putting their own lives on the line, and certainly seeing things which shock and upset them? Pay them.
Want them to work utterly unfriendly, exhausting patterns with no work/life balance? Pay them.
Because if we don't - then people won't. We need people to want to do these jobs, and we need a lot of them, so we have to make it worthwhile. The universally understood way of making something 'worth it' is the reward at the end. For a job, that's your paycheck.
It's obviously very far from as simple as this, of course, but it's also really not as simple as 'where's it coming from?'
It isn't great for inflation, though, you're right about that.