There's a happy medium achievable between the straightforward blunt instrument of cash payments and systems whose targeting is so complex nobody understands their costs or benefits.

I'm unconvinced by neoclassical arguments by Friedman et al. on "distorting" for two reasons. Firstly there's nothing inherently wrong with introducing further "distortion" into the market unless you subscribe to the evidently false proposition that no person's ability to optimise their spending habits with respect to their budget constraint can be improved upon; that you're making individuals and society worse off for buying them healthcare when they expressed more interest in a hire-purchase agreement for a state-of-the-art pickup truck. I believe quite the opposite: people receiving government money aren't entitled to spend it on anything they want, and even with imperfect information a technocrat, will often be better at allocating some of that cash than the average welfare recipient.

Secondly, given differences between incomes, propensities to consume and the ease of introducing new supply into the market, a simple flat subsidy can distort markets more than targeted payments. Converting payments such as government funded health insurance to cash would have the effect of inflating the prices of ramen and particularly crappy apartments (since welfare recipients can live without the health insurance, albeit for less long, and there's not enough decent apartments in many areas). Given the relatively fixed supply of housing, people who already owned rental property would capture more benefit than any other industry, ironically because they chose to use their capital in a relatively unproductive manner. On the other hand, hospitals might be worse off, losing part of their customer base and seeing cost increases (notably unskilled labour). Since the government has the choice in how they distort the market, I'd rather they subsidise healthcare professionals than slum landlords.

I totally agree with your point about bare minimum safety nets encouraging innovation. Even those poor who are never going to launch world-changing startups might consider a stab at freelancing in an area they're more capable in than dishwashing once the risk of not having regular income is removed.