Growing up as a wrestling fan in the 80s and 90s, I enjoyed the old-school, over-the-top characters (hence my ID). But, I also enjoy the new, realistic characters and their development. It's all about the changing times.
Back in the early days of pro wrestling and going through the years all the way up through the early '90s, before the Attitude Era in WWF/E and the nWO revolution in WCW, it was easier to have these over-the-top, cartoonish-type characters for a few reasons. Mainly, it was because there wasn't as much inside knowledge of the wrestling business by the smarts and the Internet fans. There was no way to find out what the wrestlers' real names were, the characters they portrayed before or where they worked prior to hitting the big leagues. It wasn't widespread knowedlge, which allowed for more of a mystique about them. With the advent of the Internet, you can now find anything about pretty much any wrestler out there. When wrestlers would jump ship from WCW to WWF/E, people didn't know back then until they showed up unannounced on television (i.e. Hall and Nash). Now, people know about it before the companies even know. Plus, word is getting out about people in the underground or minor leagues quicker (Bryan Danielson, for example).
Also, a lot of the people who were fans growing up got older. They became teenagers and young adults. The shift in popular culture to a more edgy, realistic view on life brought that same view to the sport. But also remember that there were always wrestlers that portrayed average-Joe types and were pretty much the same in and out of the ring (Bruno Sammartino, Vern Gagne, Tully Blanchard, Arn Anderson, a lot of guys from the southern wrestling promotions, etc.), so it's not like it just happened overnight.
So, the gradual shift turned from the bombastic characters like Hulk Hogan, old-school Taker, "The Million Dollar Man," LOD and the ilk to more realistic characters that fans could relate to better. Perfect examples are guys like Stone Cold Steve Austin, The Rock, Bret Hart, DX (as goofy as they were), and some of the WCW guys who I think basically should be credited with saving the wrestling industry in the 90s. In particular, Austin. The common man fan latched onto him and the others, and that made wrestling popular again. More and more wrestlers began making appearances in mainstream media again, like Hulk Hogan did in his prime. However, it was more "real." So, the powers that be latched onto that idea and rode it into what we have today.
Plus, with the more realistic characters, they're easier to flip between heel and face personas. Sometimes, characters would just be so locked into one side, you'd have to repackage the entire character to turn them. Now, it's just as simple as having them attack someone or give the right type of promo.
To sum it up, it's basically a reflection of modern culture as to how wrestling characters are created and pushed.