Yes, I have seen the "phenomenon" numerous times. I would not bother with checking the alignment. Remember to adjust tire pressure only while tires are cold. I prefer to do it in the morning, but I have read that if the tires have not rolled for an hour you can adjust pressure.

Rotating your tires will help alot. It can't do anything about a tire that is already gone, but it will make the SET last longer.

I went through a period of liking unidirectional tires, but that honeymoon is over. I now use tires that can be used rolling in either direction, which applies to most tires that you might buy for your Benz, and I then use a cross rotating pattern.

When rotating I cross the front two tires to the back and then move the rear tires forward keeping them on the same side of the car. In recent years I have seen lots of tires that begin roaring, mostly on front wheel drive cars, but also on rear wheel drive. Rotating the tires in this manner will go a long way toward preventing this and let the set wear out evenly.

Good luck,