Depends on the concentrator. Reflective foil or linear fresnel lenses are likely to always be far cheaper to produce per square than even the cheapest solar cell,
I admit it's been awhile since I priced linear fresnel lenses, but I seem to recall they were substantially more expensive than $25/square meter, which is about what you'll pay for a mainstream high-efficiency silicon solar cell nowadays. Could be less for the fresnel lens nowadays -- like I said, it's been awhile -- but solar cells have gotten so cheap that the sum total cost of the extra hardware associated with CPV is looking pretty high in comparison to simply adding more flat-plate solar modules.
so far nobody has spent a lot of effort developing cheap concentrator installations beyond the DIY stuff
Sunpower spent quite a lot on it in the early '90s -- in fact, it was their entire business model back then. Then they did it again starting around 2012, sinking a rather large sum into a low-cost 7X concentrator. Amonix blew through many hundreds of millions of dollars trying to develop a cheap commercial concentrating system over a couple of decades (they raised $200 million in their last 2-3 years of existence alone) and went through about a half-dozen iterations of their technology. SolFocus spent a couple hundred million as well. And when Soitec gave up on concentrating PV in 2015, it claimed to have already invested $200 million in a factory to produce CPV systems. And those are just the ones I can think of off the top of my head.
No doubt due in large part to the fact that silicon solar cells mostly don't like high concentrations of light without expensive active cooling.
No solar cells do. That's not unique to silicon. Some lose efficiency more slowly than silicon as temperature rises, but when you're talking high concentration, all cells require active cooling.
I seem to recall that there's not currently much difference in cost between a big cheap silicon cell, and one 1/10th the size that can thrive under 10x the solar input.
Maybe I'm misunderstanding you, but the way I read this, I think you're saying that a 1X solar cell with, say, 250 cm^2 costs the same per cell as a 10X solar cell with 25 cm^2 area. If that were the case, there would be absolutely zero reason to pursue concentrators at all. The whole rationale for concentrators is that you can use cheap inactive materials to focus sunlight on a much smaller amount of expensive active material than in a traditional flat-plate system. In fact, there are some slight differences in doping and contact design between concentrator and 1X cells, but that's about it. In a silicon concentrator, you'll use a bit more metal -- you need a larger cross-section to handle the higher currents -- but that's the main additional material cost. There are a few process tweaks, and you'll generally produce multiple solar cells on a single wafer that you then cut into pieces. Many of those things add a little cost, but not nearly 10X. And aside from the extra metal, those would mostly disappear with sufficient scale.
But then, CPV has some serious geographic limitations -- it's pretty useless in cloudy weather -- so it would likely never reach the scale that flat-plate PV has already reached. In terms of cost, that lack of scalability poses even more serious problems for balance-of-systems than for cells. Considering that CPV shifts cost from the cell to the BOS by design, that's really bad news for CPV.