I agree with several of your points. However, I never said she was too good for it (most pros don't need so much help from their racquet though) - the idea of her using a Babolat when she has been very successful with Tecnifibre comes out of left field. My belief is that most of the top tour players that use tweener racquets doctor it up and specialize it to their liking. I'm pretty sure Fognini isn't using a 10.6 oz unstrung Pure Drive. They become unstable when hitting a big ball from you opponent if you keep the same weight. The Pure Aero is used mostly by advanced players to increase their RPMs since it's a spin racquet. The thick beamed racquets have so much free power that it has to be reason #1 to switch to them as you are sacrificing control and feel. It goes without saying that any professional could adapt to a racquet by changing the balance, weight, strings, etc. It's just what is best for them - or sometimes it's what is best for their wallet.
Most of the WTA tour use 100 inch rackets like the vcore 100, pure aero, pure drive, and so on. Most WTA players aren't spin monsters either, but I can still see why such frames are so popular in this case (high launch angle (margin for error over net when targeting bigger spots), a lot of forgivness, more power from difficult positions, and so on and so forth). However, yes, a racket like the pure aero has been designed for spin, and a majority of atp players using such frames play with a lot of rpms. And for these players, that spin access can lead to more control when hitting big. Spin can be control.
With this type of racket you must bring your own control in the same way you must bring your own power with a thinner more flexy beamed racket with a smaller head. It goes all ways. I think sometimes we forget that every element within a setup (weight, swing weight, balance, beam thickness/shape/stiffness, head size/shape, and so on) will help and hinder different aspects of our games. A pure aero brings with it more inbuilt power than a blade, but a blade brings with it more accuracy and acts against the players swing to help them keep balls in. A pure aero is not a racket for a player that doesn't bring their own control (unless we're talking beginners to intermediates). And a blade isn't a racket, at least generally speaking (at largely at competitive levels anyway) for a player who can't bring their own power.
For advanced players all the way up to pros, the reasons to use a tweener are varied. Some players, even elite level ones, don't pack enough of a punch at their level so a racket like this can help them (same way that an erratic ball striker would be helped by a control racket or a short player being helped with an extended length racket). Some players play with lots of spin, and therefore a high launch angle and easy access to spin enhances their strengths and allows them to swing harder with more security, so it's less about power in the sense of helping hit winners and more about how that power goes into RPMs and makes for a heavy ball (I think in many cases you get more power, with proper technique, from control rackets, at least in terms of through court winner style power). In some cases it's building on an already powerful game to kind of go all in on that, like with Berretini for instance (Head Extreme), although in his case he's already benefitting from the high RPMs helping him keep those massive bombs in the court. I'm sure most wouldn't say that Berretini needs power or lacks it, or Ruud or Nadal and so on. There are other reasons a player may choose such a racket. But in most cases it's not because the player lacks power/needs help with power, the same way extended length rackets are popular among big servers for example (I don't think Isner needs help with his serve, but making it even more effective isn't a bad idea).
Feel is very subjective.
Re customising a racket/setup to their liking, most pros, at least higher end ones, will be doing that. I imagine it's very rare for higher ranked pros, let's say top few hundred, I don't know, to be using stock rackets. I also find it hard to imagine many players at that level swinging a 95 inch racket that weighs 305 grams and has a swing weight under 320 and an RA under 65 say. That's a recipe for no stability. Thicker stiffer beams and larger head sizes will generally provide more stability at lower specs, so they don't necessarily need to be as heavy. They are also powerful so they don't have to be as heavy to generate pace. On this note, most higher pros I'm aware of who use smaller head sizes and thinner beams have higher static and swing weights. Sampras with his 85 inch pro staff had a massive swing weight and static weight, so it was certainly not lacking in power. So the power with such setups can come from that, which is why commenting on the power of a pure aero at that level isn't so simple. If you've ever tried the RF97 for instance, it's more powerful than a stock 300g pure drive if you have the technique to swing to it.
With non pros, many at least, rackets are bought at similar specs and don't customise them. So control rackets and power rackets, I feel in a way there's more of a contrast there than for a top pro, where a top pro using a control racket might have beefy specs to give it that power and a top pro using a spin/power racket may use it at slightly less beefy specs to gain say more racket head speed and spin. Not necessarily like that though. As I said, styles and swing styles and such.