Apple wants money, after they get it, why do they care if customers are happy or not? So far, they knowingly slowed down people's phones without telling them what was going on. Why would a company who wants happy customers do that? Apple's actions did just prove it.
Maybe Steve Jobs wouldn't have done that, but now there is a different person running the company.
Steve Jobs started the whole "You are verb-ing it wrong" meme.
And a happy Apple customer stays an Apple customer. Apple has many ways of monetising their user base after the sale of the initial device, from getting them to purchase additional Apple products, to App Store sales, to iCloud subscriptions and Apple Music. Heck, Apple even gets a tiny cut of every Apple Pay transaction you make. They have every vested interest in bending over backwards to keep you as the consumer happy so you will continue to buy more Apple hardware, not throw you under the bus once the sale has been made.
Apple slowed down people's phones precisely because they care that their customers are happy. If you look at Android phone-related threads on Reddit, you see people complaining about how their LG phones bootloop, or how their Nexus 6Ps keep shutting down or restarting themselves, particularly when they are in the midst of an important task such as calling emergency services, and you know that they are never ever going to get a patch of any sort to remedy this. Apple made a judgement call, and decided that random shutdowns was wholly unacceptable, and that throttling your phones was the better solution out there. Not saying it's a good one, but the other solutions all have their limitations, and I can understand why Apple ultimately did what they did.
For starters, the iPhone was not designed with user-replaceable batteries in mind, and it likely never will be, so while a few posters here have taken it upon themselves to swap out the batteries inside, it's not something they expect their users should have to do.
Meanwhile, changing iPhone design to include larger batteries (iPhone Plus models don't appear to suffer as much from this throttling issue) is a longer-term design consideration. We will have to see if the stacked battery design of the iPhone X and rumoured X+ ameliorates this issue any. An improved power delivery system is also an additional longer-term consideration (earliest 2019 if the rumours are to be believed). I believe Apple is and will eventually work towards this; it just won't be available anytime soon.
Third, a pop-up of any nature is just going to result in unnecessary misinformation and panic amongst the majority of Apple users. People are just not going to have sufficient information anyways to make an informed decision on what they need to do. In addition, it is simply not acceptable to leave it up to the user to choose between experiencing slower performance because of throttling and just having the iPhone shut down.
Lastly, even this battery replacement programme is not going to be accessible to every user, especially those who live in countries with no Apple store. I suppose now that the news is out in the wild, they could have have the battery replaced themselves or at a 3rd party repair store, but then they take on the risk of accidentally damaging their phone every time they crack it open to service the internal battery, and Apple is not going to be there to bail them out if this happens.
This leaves throttling as a legitimate option with the best risk/reward in terms of the user experience. Every other option, including sending an iPhone away for a battery replacement, results in a major user experience tradeoff. And Apple is all about the user experience. Sometimes, you just can't win. You can only select the option which minimises the losses.
And for the record, I don't think this iPhone throttling issue will send people to Android either, though we will have to wait to see what the impact to Apple's reputation will be, if any.
In the near-term, I agree Apple should provide a clear and extensive explanation on what exactly is going on (what they have done is a start, but still not quite near enough). I believe this will go a long way towards stopping the bleeding as most people will eventually see that Apple is being rational and is genuinely looking out for the user. Apple can then assess where additional information about the battery and throttling can be included in iPhone settings (there is always that eternal dilemma between too much information and too little).
Just my 2 cents, for those who care enough to read.