There are actually many different breeds of roaches depending on the location. While most cockroaches are scavengers, a minority of these pests is also wood-eating, exactly like termites. Termites can breed much faster and in greater quantities than cockroaches however. This is precisely why termites are potentially the greatest threat when it comes to a pest infestation. Actual structural damage that can cost you tens or even hundreds of thousands almost always stems from a termite infestation. Compared to this, roaches would be a mere annoyance.
Sure, diseases can be spread by roaches, but such cases are rare. If left alone however, roaches can easily lay up to 100 eggs a day, in a single sac. And with multiple sacs in multiple locations all over your home you’d be dealing with a massive influx of roaches if you leave them alone. A dilapidated building that is left alone for a mere 3 months can lead to multiple infested locations in the entire area. Since roaches are also known as some of the most resilient pests, they can easily survive in any environment, even one that’s devoid of food, for over a month. Cockroaches also always leave faeces wherever they go. This sort of allows the other roaches to follow the ‘trail’ that it leaves behind, thereby causing a small infestation to be much worse the longer the period of time.