>building a brand (your or your company's) This is exactly correct. It is "Hey potential employer, check out my Medium articles." Sure you could host it yours

>building a brand (your or your company's) This is exactly correct. It is "Hey potential employer, check out my Medium articles." Sure you could host it yourself, you will probably pay a monthly fee for this. Also people you are marketing to would most likely go "Oh hey, this guy is Medium, I have been on that site before." Opposed to "Oh this guy is on some blog platform I have never heard of."