Both chemical methods and ultra high-pressure water can be used. The chemicals (at least the ones that work well) are ecologically unfriendly. The high pressure water is specialist equipment - not just the fire truck's high pressure hoses. Slow process. Not especially cheap or expensive, but about $US3 per square metre (say $50,000 for an average runway for the two touchdown areas + mobilisation of $10,000-$20,000).
The rate of rubber buildup is proportional to the number of landings as one would imagine, and there are various rules (especially FAA) about the frequency that the runway should be inspected. Removal periods can vary from once a year to more than once a month. At over 210 landings per day, the friction should be tested weekly. Where I am today (YBRM) which is pleasantly quiet, they wait for the annual wet season to wash the rubber off.
Friction is best assessment method. A runway that is white (such as concrete or a bitumen/asphalt with a white coloured aggregate) looks much worse than a black runway with the same friction degradation.
Why would you leave a runway uncleaned beyond any reasonable limit - lazy? incompetent? too hard to arrange to fix? on an island and the high pressure truck has to come by ferry and it won't come for another 2 months then the tourist season is over anyway so why bother and now it's lunchtime so I am off duty?