Sorry, did you never see Leela or Peri’s getup? Or how about Dodo’s, or Zoe’s (and frankly hel-looo Mary Tamm and your wonderful white dress) and any number of girls-of-the-week? You may have also missed where several companions fall in love (that’s romantic love, not platonic) and leave the Doctor for those people, or the romances between Ian and Barbara (first companions jsyk) and Jamie and both Vicky and Zoe, or the flirtation between Sarah Jane and Harry, and if you didn’t ever find Jo and Peri flirty I’m not sure what show you were watching. Also, maybe you missed the series of commercials that played up the Doctor and Romana’s close relationship to the point where he proposes to her? Also, there’s the time when his first self gets engaged to a lady who seems very taken with him, and there was his second self’s doppelganger who seemed to be implied to be pretty active. Let’s not even get into the number of times his companions have been seduced and bewitched in suggestive ways over the years, either.
Here’s why the girls weren’t all over the Doctor in the classic series: BBC had a ban on the Doctor kissing or being romantically involved with anyone, especially his companions. Here’s why they are now: The ban is lifted.
And it’s not just the ‘newest’ version that has the Doctor macking on companions. He kisses Grace twice–I think actually three times–and flirts with and woos her all movie long. And if you’d read the novels, you’d know that Eight and Bernice did a whole lot of 'shaking hands’ upstairs in a bedroom together.
The Doctor getting all the attention he’s getting and there being young flirty girls is nothing new to the Doctor Who fandom, it’s just that in today’s society they’re allowed to actually SHOW it, instead of implying it or keeping it mostly off screen or restricting it only to companions. Sure it’s not 'based’ on sexual relationships, but there’s ALWAYS been room for them, so no, they’re not in any way out of place in Doctor Who or its characters now.