> But what does he mean by "Objects" and "Classes"?
To be hones, I'm not sure.
> Everything good about objects that a pure functional programmer would want is captured by first-class modules.
I just know that in the talk I linked above, Odersky mentions 1ML, that it converts modules into SystemF (extended Lambda calculus, but you probably already know that) and that he feels this attempt is force fitting where some (important?) things get lost in the conversion.
From 2:56 to 4:55
> The internal mutable state
That is very strongly discouraged in the Scala community.
> subtyping
Yep, that is embraced quite a bit.
> inheritance
Used to some extend but still generally discouraged even though not as strongly as mutable state.
> ... relationships are much less useful
How can you say that subtyping is not useful? In Scala it is one of they key ingredients for modularity. You have signatures (aka interfaces or traits) and than you have multiple implementations (modules, objects, classes as partial abstractions) which you can swap one for each other. That is possible because they form these subtyping relationships. A side note: Scala code which embraces subtyping has better type inference.
> But please do take a good look at Haskell too, if only just for interest.
I don't want to make an impression that I want to offend the Haskell community. Haskell is where I learned FP and the languages is a great success in many regards. Over Scala it has many advantages, like better syntax, better type inference, better control over memory layout, better optimized which turns even advanced idioms into efficient code, etc.
But it also has some downsides compared to Scala. It is lazy which makes debugging more complicated. It doesn't have any satisfactory modularity story (last time I was around there was Backpack, but it hasn't caught on AFAIK). And Scala has all the advantages that come with the JVM and Java interoperability: great debugging, profiling, introspection, telemetry, etc, great IDE, huge gallery of libraries, etc. I'm a software engineer and all these things are _very_ important to me. Compiling to efficient JavaScript with Scala.js is also nice.
> Many leading Scala programmers ended up moving to Haskell, in order to get deeper into FP.
Sure, if you want to write Haskell programs, you'll have much better time in Haskell than with Scala. There were people like that, and so they eventually left. But note that you can be deep in Pure FP in other languages, like Scala or PureScript, Haskell is not the only game in town, each comes with its pros and cons.
That being said, with Haskell, Pure FP is built right into the language. With Scala, while easily possible, Pure FP is built on top of the language with library(-ies) and that comes with some disadvantages.