Why not? The Doctor is hundreds of years old. By comparison to him, twenty-somethings like Amy and Clara are practically children. Eleven hung out with Amelia Pond and Kazran Sardick as kids, and he seems to be the most child-friendly version of the Doctor (I'm looking at you, Sarah Jane Adventures and Stormageddon). Besides, the Doctor gets a kick out of watching people's awe, wonderment, and imagination... I'm almost surprised that the Doctor doesn't hang around with kids more often.
Does he, though? Pretty much every woman that Eleven has had around has been at the centre of some sort of mystery. Amy had the crack in her wall, and then turned out to be central to the Silence thing. River Song is obviously a mystery from start to finish. Clara is a mystery. He hung out with Craig Owens who, though not female, was sort of caught up in a mystery. The Doctor's Wife was all about Eleven and a mysterious woman. The Beast Below had Eleven and Liz 10, another mysterious and intriguing woman. The Doctor, the Widow, and the Wardrobe... a woman at the centre of a mystery. When we first saw Oswin before we knew she was Clara... mystery woman. Eleven certainly has a type.
Sure, we know that Eleven took River on dates. There was Stevie Wonder under the bridge, and other stuff. But then, he also had "dates" - or at least, "adventures" - with the Ponds, coming back every few months so they could have some semblance of a normal married life. He's having "dates" with Clara, coming back every Wednesday (or whichever day of the week it was). It seems like Eleven has adapted: instead of a constant live-in companion, he's using the TARDIS as a fast-forward button to let people have a life without him while he has a constant stream of adventures.
As far as being a mystery goes, River has been "solved". Their lives were moving in opposite directions, and while yes they got married... that was nearly the end for Eleven, and nearly the beginning for River. The last outing for the Ponds is an exception, and this episode (which is apparently set after Silence in the Library from River's perspective, and was originally titled "The Funeral of River Song") has the potential to be about getting closure on that character/arc.
So yeah, the Doctor loves River. But he loves all his companions. And he loves a good mystery. The Doctor knows that River is destined to die, she gave up her regenerations so she only has a mortal lifespan... that relationship was over before it began, really.
I guess that, because the Doctor got over Rose (who he loved), it doesn't necessarily strike me as out of character that the Doctor is moving on and flirting with the next mystery, even if I don't necessarily approve / like it.
Edit:
So, here's a random thought. The Doctor Who franchise used to have The Sarah Jane Adventures catering for young children. Series 7 is the first Doctor Who series to come out after that finished... and we had episodes about dinosaurs and cowboys, as well as a bunch of episodes with Clara that are "less complex" than what we're used to from Steve Moffat. I wonder if there's been a conscious choice to make Doctor Who more "family friendly" again.
Viewed through that lens, Rings of Akhaten is a story about how it's okay to make mistakes, and how you can resolve things by talking instead of fighting. Cold War was a history lesson: it explained the cold war and the idea of mutually-assured destruction in a way that was relatively easy for children to understand. Hide is a story about how love conquers all, and about misconception: the ghost wasn't actually a ghost, and the monsters just wanted to be with who they loved. Journey to the Centre of the TARDIS had that "don't be mean to your brother" morality thread. Crimson Horror and The Snowman both have a same-sex interspecies marriage that no one bats an eyelid at (rightly so), and the only people who seem to have a problem with it (the Inspector at Christmas; the fainting man the other week) are painted as comedy figures that no one should want to emulate; Crimson Horror also had threads about acceptance, disabilities, the sins of the mother, etc.
Maybe I'm grasping at straws... but if the BBC is trying to make Doctor Who a little more kid-friendly to compensate for Sarah Jane Adventures not being around any more, the creative / story decisions this year make a lot more sense.
Edit 2:
Holy shit, did not realise the Captain was Tamzin Outhwaite. HOW DID I NOT REALISE THAT?!
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