My impression of what happened was that the iPhone replaced Flash, and therefore HTML5 couldn't replace Flash because Flash was already gone.
There were some nasty things about Flash, but in retrospect mobile applications are so much worse. We used to have things better than we do now.
Not really. Flash was terrible on phones that supported it. There were SDKs that turned Flash applications into native iOS ones, IIRC, but otherwise Flash was a dead end once mobile started to grow.
I was on Adobe's community advisory board at the time of the iPhone fight against Flash and I'd work with all sorts of things that were supposed to be for the phones.
Flex had problems with phones. Macromedia and later Adobe built this GUI framework on top of Flash with multiple problems... performance being one of them, but the other, and perhaps more important problem was that Flex was created by people who wanted to copy Swing. In no way was it any good for making typical smartphone UI.
So, Adobe tried, but with very little commitment to produce some sort of Flex-based "extension" for smartphones... and that thing never went beyond prototype. Also, at that exact time, Flex was transitioning to using the new text rendering engine, which while offered more typographically pleasing options was really, really slow to render.
People behind Flash player had some good ideas. Eg. Flash Alchemy: a GCC-based backend for ActionScript that made Flash very competitive performance-wise (but never really went beyond prototype). Around that same time a new UI framework appeared in Flash aiming to utilize GPU for rendering, which was a big step in the right direction, especially considering how "native 3D" in Flash failed (it was all on CPU, operating very heavy display objects).
None of these ideas saw much traction in particular because Adobe's management responsible for the product lived under illusion of invincibility. They did a little bit of something, just enough to keep the lights on, but they didn't realize they were side-tracked until it was late. And even at the time it was late, they made some really bad choices. Instead of open-sourcing the player, they started a feud with people who wanted to maintain Apache Flex (the Adobe-abandoned Flex) because of some irrelevant IP right on the Flash player core API. They never officially recognized Haxe. And, generally, undermined a bunch of other projects that targeted their platform (Digrafa comes to mind).
They didn't come clear with major users of their technology, repeating "Adobe is eternally committed to supporting Flex" until they left it in the ditch and forgot all about it. They made it very, very hard to support them in whatever they were doing.
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Bottom line, Flash could've been made to perform well on smartphones. It ran OK on what would today be called "feature phones" before smartphones existed (eg. it was available on Symbian), if you knew what you were doing.
It died because of piss-poor management on one side and monopolistic desires of mega-corporations on the other side.
Come on… I was around at the time and played with it on phones that supported it. From a user’s perspective it was very bad. Some people desperately wanted it to happen and they had their reasons, but saying that I am negative without having tested it is pointless speculation, and wrong.
When Android just appeared on the market, I worked for a company that was making a video chat Facebook app. It was written in AS3 and one of the main features was to apply various effects to video. We tested it on Android, and it worked fine, even though that's a very memory and CPU intensive app.
Really, Flash player was not the problem. It couldn't go toe-to-toe with native code, but optimized AS3 code would beat unoptimized native code.
It was some form of code-golf to write Base64 encoding in AS3 and benchmark it. Usually comparing to the implementation in Flex. When Flash Alchemy came out, I wrote a version of Base64 encoding that beat it something like 100:1. A friend of mine who was known by his forum / Github user name "bloodhound" (here's some of his stuff: https://github.com/blooddy/blooddy_crypto/tree/master/src/by... ) wrote a bunch of encoding / decoding libraries for various formats (he also improved upon my Base64 code). And these were used all over the place for things like image uploads / image generation online. This stuff would beat similar Java libraries for example.
Not sure if you remember this, but at one point in the past Facebook had a Java applet that they used to manage image uploads to your "albums". Later they replaced it by Flash applet. It didn't work any worse that's for sure.
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The performance problems were in Adobe AS3 code, not the player. Flex was a very inefficiently written framework. And so were AS components. But if you take AS3 3D engines, even those that were fully on CPU... you had plenty of proper 3D games. Eg. Tanki Online (a Russian game made with Alternativa3D Flash engine) was a huge hit. Even if the phone could handle a fraction of that, you'd still have plenty of room for less complex UI.
iPhone browser, like MacOS browser, drop support for Flash (and most plugins in fact but Flash was the most noticeable.) In the other hand, HTML5 was adopted quickly by Apple. So we can say that HTML5 replaced Flash (not iPhone per se, as it didn't come with a specific replacement first and an alternative was already there second.)
However, I wouldn't say that HTML5 is the drop-in replacement of Flash. It did help to avoid this later on some common use cases with video and audio tags and standardisation of formats (that also kill use of QuickTime/WindowsMedia/RealMedia plugins)