Giménez has leadership mentality, too - he was the defensive leader for Uruguay in 2013 when they reached the U-20 World Cup final and conceded just 3 goals despite being the youngest player in the unit. At Atlético, he doesn't get to display his leadership traits because of the presence of Godín (arguably the best centerback in the world), Juanfran (top 3 rightback in Europe), Luís (top 3 leftback in the world), Gabi, Koke, Griezmann and the likes. He's not going to stand out as a leader, especially in that defensive unit with contemporary defensive behemoths flanking him and exerting their influence on the team. Expecting him to be a leader in that backline would be like expecting young Terry to be a leader in a hypothetical backline consisting of Blanc, Thuram and Lizarazu - it's not going to happen, and is all about relatives.
Regarding the proven and top centerback bit, that would be ideal. But just to reiterate what was said before, outside of the likes of Godín, Bonucci, Thiago, Boateng and the likes, there aren't a lot of proven and top centerbacks in the current market. Apart from them, you have the likes of Alderweireld (likely unattainable), Manolas, Van Djik, etc. - who aren't much better than Giménez, and some of them haven't evidenced the ability to lead the defense for a team of United's stature, so we have to adapt to the market. Leading a club like Southampton is very different from leading a club of the dimension of United - which is partly why someone like Schneiderlin was their midfield leader, but that didn't amount to much at United.
I think the perfect player for United would be Sokratis Papastathopoulos - who has played a big part in maintaining Dortmund's defensive structure - he could come in and be exactly what we need because he has played for a big European team for 4 years with ~30 European appearances, and has become their leader after the departure of Hummels. But they are not likely to sell them because he's a key defensive presence.