I'm actually glad I was embarrassed by my parents when I was growing up, more specifically by my dad. My dad is that kind of person that brings an air horn and big, flamboyant homemade signs to awards ceremonies, sports games, banquets, etc. Although I have to admit, him being a distraction during sports events was really annoying at first. Concentration is important for any sport, and he was breaking it. But I'm still glad that he did it. Why? Because he taught me how to block out everything around me while I was playing sports. If I could block out him screaming on the sidelines while blowing the air horn, I could block out taunts from the crowd and other players, and practically anything else. In his effort to support me, while also embarrassing me, he built up my ability to concentrate, and therefore, made me a better athlete.
Not only am I now able to control my concentration, but the embarrassment I experienced also helps my professional life as well. Since my dad was clearly never afraid of the spotlight and had no problem pulling me into it as well, it led to me building strong and lasting characteristics. My tolerance to being in the spotlight and endurance to typically flustering situations increased. As a manager, I run into some frustrating situations here and there, which can lead to me being the center of attention as my staff and customers look to me for guidance, or in other cases, the customers seek me out to fix a problem (which they're not always nice about). Having a long history of dealing with flustering events, work problems don't phase me.
Embarrassing your children can actually lead to positive effects on their future. As long as you're not doing things too extreme to an inappropriate level, it should be OK. Tolerance and endurance are very important mental characteristics to have as a growing adult, and I credit childhood embarrassment for that.