They cause a great deal of stress. Idols are constantly worried about their safety and privacy. For example, if they know there are sasaengs following them all the time, they can't relax even in their free time.
It can also affect their mental health. Constant intrusion from sasaengs like having their personal space invaded, receiving creepy messages or being stalked can lead to anxiety and depression. Many idols have had to seek professional help because of the sasaeng - related problems. They might start to avoid public places or interacting with fans in general, which is a pity as most normal fans are great. And in extreme cases, it might even make them consider quitting the entertainment industry as they feel there is no way to protect themselves from these sasaeng horror situations.
Financially, it can also be a burden. Idols may have to spend a lot on security measures such as hiring bodyguards, installing security systems in their homes and cars. This is all because of the potential threats from sasaengs. Their managers also need to allocate more resources to deal with sasaeng problems, which could have been used for other aspects of the idol's career development like promoting their works or arranging better training.