Do landing strips suffer from landing wheel tire tracks?
It does indeed degrade performance, and runways (and their lights) have to be routinely cleaned of rubber. The FAA specifies safe friction levels.

Wikipedia has this to say:


  The build up of rubber affects the level of friction of the runway, most noticeably as a reduction in braking and ground handling performance. This can lead to incidents such as runway overrun or a lateral slide off the runway.


Some runways are particularly poor: