Most residential solar installations in the US are grid tied, meaning that excess generation heads out onto the grid (this is counted as a credit under net-metering regimes). This explains why AC inversion is required. Since most solar production is midday and most household electricity use is in the morning and evening, this arrangement allows for a net-benefit to the homeowner (and to some extent the utility since daytime electricity is more expensive for market-based customers than nighttime electricity for regulated-rate-payers). Otherwise you have to store the electricity and that is expensive and very inefficient.

There are other concerns as well (e.g. no standard DC outlet, most AC appliances with DC motors would have to be modified, there would then be two electrical standards in the house since DC is still not suitable for most transmission or distribution needs, firefighters would need to be retrained, etc).