It's only a bad thing if the detail in the blown areas is important to you.

There are situations where at least small areas of blown highlights are impossible or impractical to avoid: when specular highlights from reflective surfaces, car headlights, the sun are included in the frame.

There are also times when you may choose, for artistic reasons, to make use of, or even exaggerate, blown highlights. For example high key or backlit portraits

e.g. https://commons.wikimedia.org/wiki/File:Bettina_Kenter_(High_Key_Studie).jpg

Similarly, while it would certainly be said that camera shake or blur is "bad", it can be used for artistic effect (see ICM - "Intentional Camera Movement")

e.g. https://en.wikipedia.org/wiki/File:Bluebells_ICM,_Ashridge_Estate,_2015.jpg

So to say that they are "bad"? Well that really depends on what the photographer wants.

If you do have blown highlights, your options may be limited as to what you can adjust later.

For example, here is an example of a JPG shot I took about 10 years ago before I started shooting raw.

If I apply a graduated neutral density filter to the sky, I can get more detail and contrast in the mountains and sky, but the clouds are all blown. In the cloud to the left, every pixel has a value of 255,255,255. So whatever I do, I'm going to end up with the clouds being a solid blob of grey or white, with no detail.