Sponges, especially large and thick ones, are extremely porous and have an incredibly high surface area. The more surface area there is, the more space bacteria has to grow - especially because a sponge likely has bits of food debris lodged in it to feed them. This also makes it difficult for detergent to fully penetrate every nook and cranny, and a high bacterial load, combined with the large amount of lipids typically present in food, will very rapidly "use up" all available detergent in the sink.

I wouldn't resort to cooking my sponges though - I don't like the idea of broken-down plastics and petrochemicals from synthetic sponges making it onto my plate. Letting a sponge completely dry out between uses is pretty effective at killing germs, and always make sure you use lots of detergent when washing your dishes. And yeah, regularly switch to a new sponge.