... ultimately, you still need tax rises or increased borrowing at some point to "pay for" increased public spending, unless you think it's no problem that the debt (and interest on that debt) continues to increase forever (which is not to say there shouldn’t be a debt at all—as per a household—just that there is an optimal range which the debt should fall in).
MMT doesn't really claim that there is a free lunch, in my view. Instead it claims that it's worth considering that the cost of the lunch could be much cheaper.
I'll try to explain by way of analogy. MMT says that the economy is like a household where there are depressed teenagers lounging about. The teenagers represent the unemployed and the underemployed. At the same time, the house needs loads of work, the youngest child needs babysitting, Grandma needs looking after, etc. One day, the parents hit on an idea: to write IOUs for work done. To stay in the house, the teenagers need 20 IOUs a month.
What happens? The house gets painted, cleaned, maintained and improved. Granny and the youngest child gets looked after. And lots of this gets done for no cost (or negligible cost), because it uses resources that were under-used. To this extent, MMT says that there are some almost-free lunches to be had - employing unused resources just has to be better than leaving them idle.
Is everything an almost-free lunch? No - the household doesn't have all the resources it needs. The household needs to buy the paint to paint the house, etc. So, the parents need to understand what is 'free' and what creates obligations that need paying for. This is - in an imperfect analogy - the central message of MMT. It doesn't say that all obligations created by fiscal spending are free - it says that governments are not fiscally constrained. The constraints are elsewhere - inflation and real resources. So, returning to your post above, of course you need tax rises at some point to create the fiscal space for government spending. That's consistent with MMT as I understand it. It's just that MMT talks about tax rises to control inflation. Either way, it amounts to much the same thing.
The absolute size of the deficit in any period, though, and debt-to-GDP ratios maybe don't tell you much, as long as - crucially - the government is directing its resources responsibly.