Yes, I think that the government should build roads. Some states are apparently not concerned with the safety of their citizens. This is evident through the damaged and sometimes dangerous road conditions found in some states. If the states are not taking the initiative to improve their roads then the government should step and in and fix the problem.
We do not need a government to build the roads.
Roads existed before governments built them. There were private highways. There are examples (type into Google) of highways existing now without a government building them.
The Government has no incentive to keep the roads as efficient and economical as possible. They will just take taxpayer money to build more. If it was profit driven, they would ensure the highest quality roads for the quickest travel, and quickest travel to ensure the least wear and tear.
They would also allow bids for others to build the roads for them, unlike governments who usually dole it out to their well connected friends or government workers with no bids.
Is question: Is there a demand for roads? YES! So, someone could make a (large) profit to build the roads. So the roads would be built without a government.
Example: The oil companies need people to consume oil and gasoline. They would have a massive incentive to have roads for people to drive on. Instead of lobbying the government to build roads and Interstate Highways, and lobby government to disallow green energy companies tax breaks and other incentives to compete against Big Oil, they 'could' build it themselves.
People often speak of the effects cars have on the climate, and a large part of this problem is due to the emphasis the government spent on roads; governments, in effect, subsidized driving with many cars on the road. Private developments build roads themselves often, and poorer areas, except for cosmetic reasons, often don't even need roads (fewer cars).