Naively, yes, diversity avoids systemic risks. However, from working in auto insurance it was my experience that insurers reason about risk in considerably more sophisticated ways.
For one thing, in the US auto insurance is entirely a state-by-state market. This means that geographic diversity is inherently severely limited. Any auto insurance operation in California is going to be exposed to a lot of wildfire risk without the ability to geographically diversify. This is priced in.
For another, there some groups of people - remember auto insurance is really mostly about insuring people - who are statistically more expensive risks than other groups. Young men are measurably less safe drivers than middle-aged women, to pick an anodyne example. Individual premiums reflect this as well. I have no idea what kind of systemic risk would uniquely affect all middle-aged women across an entire state, but presumably you can think of one.
Most insurers have groups of customers they would prefer not to have. This is usually because the insurer cannot cover them at cost, never mind profitably. There's a series of ways they encourage those customers to find other carriers. This is where the idea of maximizing diversity breaks down most clearly - the overall risk pool is not improved by including these customers.
For one thing, in the US auto insurance is entirely a state-by-state market. This means that geographic diversity is inherently severely limited. Any auto insurance operation in California is going to be exposed to a lot of wildfire risk without the ability to geographically diversify. This is priced in.
For another, there some groups of people - remember auto insurance is really mostly about insuring people - who are statistically more expensive risks than other groups. Young men are measurably less safe drivers than middle-aged women, to pick an anodyne example. Individual premiums reflect this as well. I have no idea what kind of systemic risk would uniquely affect all middle-aged women across an entire state, but presumably you can think of one.
Most insurers have groups of customers they would prefer not to have. This is usually because the insurer cannot cover them at cost, never mind profitably. There's a series of ways they encourage those customers to find other carriers. This is where the idea of maximizing diversity breaks down most clearly - the overall risk pool is not improved by including these customers.