Should a POTUS be just like the common man?

Forgive me as today I go off completely on a personal musing. While I never apologize for my bias on this site, I normally stick to events or news as a topic. But today I'd like to just think aloud as it were. I'm not going to condemn or condone Mitt Romney today, but instead, just analyze him from a distance.
I've noticed in the past the media calling upon Romney to own up to his wealth, and to not act like he's not a wealthy man. They have asked him on multiple times to be more genuine, and say he has a connectivity problem. Even as a Romney supporter I have noticed this as well. There is always that question of when he is going to let loose and just be a regular guy. I'm wondering why this is so important to voters. Do we have to identify with the President? Why do we feel this need for him to be our best friend? I think part of it, a large part of it, comes from Bill Clinton, George W. Bush, and now President Obama. Clinton really changed the face of the presidency with his southern drawl, aw shucks personality, and approachable style. Even as his weaknesses were exposed during the scandals, it made him less elite, more normal. If he could reach the presidency beginning with his humble footsteps out of Hope, AR, anybody could. He clicked and connected with middle America. George W. Bush obviously ascended with a legacy. But again, many people identified with the father-son legacy, and that made people like him. And maybe he wasn't the guy next door, and he sure made a lot of gaffes, but, who hasn't said few dozen stupid things in their lifetime? Again, his weaknesses subconsciously made people like him. And then there is Obama who pretty much runs on the common man platform. He drinks beer, goes to his kids' basketball games, and his wife is photographed at Target. People identify with him.
And then there is Mitt Romney with his wealth of millions, perfect wife, perfect sons, and perfect hair. People don't identify with him, or at least, very few people do. There isn't a story line there to grab on to.

Except for this week when there was- he was speaking in Michigan to the Detroit Economic Club. He said, "I like the fact that most of the cars I see are Detroit-made automobiles. I drive a Mustang and a Chevy pick-up truck. Ann drives a couple of Cadillacs, actually. And I used to have a Dodge truck. So I used to have all three covered."

The Romney campaign later said Ann Romney drives two Cadillac SRX’s (model years 2007 and 2010), one in California and one in Massachusetts.
I looked up who belongs to the Detroit Economic Club- "With nearly 3,000 members, the DEC attracts high-profile individuals who engage in the great issues of our day. Membership is open to all who share a passion for business, a thirst for knowledge, and a desire to be on the forefront of the important business and political issues of our times."
Let's see, you're in Detroit, talking to the biggest businessmen in the city... Yes, you are talking to car guys.
Now, take his quote out of the room and toss it to the every day Honda driving, commuting, working class American, and no, Romney's comment isn't going to win him any friends. But when he's in that room? He just told the people who built those cars he bought some from them. He connected in the room.
Which is what got me thinking about the supposed Romney "gaffes," and all these calls for him to identify and connect. When he says that he has friends who are NASCAR owners, he means it. I think we may actually be seeing Romney not hiding his wealth anymore. This may actually be a new strategy emerging.
We used to have wealthy presidents- JFK, Roosevelt, and even Reagan. (I hesitate to throw in the Bush family there. There are too many misconceptions about their money.) In fact, most presidents prior to Clinton were men of a somewhat wealthy standing. (Shall I remind everyone we even had a Rockefeller as a VP at one time?) So why do we now almost demand that our candidates be less-wealthy, and more common?
I'm not saying I am not one of those people. Like I said, in spite of being a Romney supporter, I do feel that disconnect as well. But it doesn't stop me from voting for him. I can't help but wonder why we want to have that connect? When did we stop putting the president on a pedestal and ask him to be like us? And do we really think that is wise? I don't want my president to be just like me. If i wanted someone like me in office, I'd run myself. Maybe I'm still holding on to an old-fashioned value, wanting there to be an elite upper class. I want to have something to aspire to, to look up to. My American dream isn't one where we are all equal. My dream is where I'm working hard to achieve more, and I want someone above me to set the standard and pave the way. Maybe I am alone in that now. Do Americans really want what Occupy Wall Street is selling where we all have the same amount of everything? Do we want to lose the pinnacle and settle for a tableau?