Concrete vs asphalt pavements
Concrete pavements have high initial cost but low ongoing maintenance costs. That said, when they eventually do fail, they are very high cost to rectify as you have to replace the whole slab. They are usually only used for very high traffic roads where the cost/benefit can be justified.
Water sitting on the pavement can be reduced by making the crossfall a bit steeper or cutting lateral grooves into the concrete. Grooves increase the noise though so are no good near residential areas.
You can put a bitumen surface (asphalt etc) onto concrete, you just have to be VERY careful how you bond it to the concrete. Usually the bigger problem is any cracking in the concrete will refect straight through the asphalt to the surface.
To significantly reduce vehicle spray when wet, you can get asphalt surfaces that are porus, the water basically flows through the asphalt mat (usually about 50mm thick) and runs off the road to the side "though" the asphalt. There is no water left sitting on-top of the asphalt to cause vehicle spray. It is very expensive but is used on motorways wher traffic vol is high.
Different colour linemarking (ie yellow) can also be used to make them more obvious when the pavement colour is light (ie concrete or some granite seals). Main problem is that the colour pigment in the paint ups the cost by at least 30%.
I would not have though concrete cancer would be a risk with concrete pavements. There is very little steel reinforcement used (if any) and there is generally a huge cover thickness, so water penetration to the steel to cause corrosion is generally not an issue.