You might want to read more recent guides!
For SAP HANA modelling the direction forward is to use only calculation views.
Over the last SAP HANA releases, calc. views had been enhanced with nearly all features provides by attribute and analytic views and even an automatic conversion into calculation views has been provided.
The WebIDE - which is the strategic IDE for SAP HANA - always only supported calc view modelling.
So, if you create models in SAP HANA you should use calculation views.
Now, CDS is a very different thing.
With CDS you get the option to model the complete persistency for your data objects, including the intention/semantics for each table, column, view and reference in one place. So, unlike with bare tables and calc. views, you don't have to specify over and over again that e.g. BELDAT is a date column (even though it's encoded as a character column). You just define the semantics once.
And this is a very important aspect of CDS: you not only define how the table or view looks like and works on the DB level, but you also define how it can be consumed. For the upper application layers you really define data services that can be used without having to repeat the definition of the data design over and over again.
In this way, CDS is a lot more powerful than simple SAP HANA DDL.
Now why didn't SAP HANA live use it then? Because when SAP HANA live was first created the available CDS implementations and tools hadn't been ready yet.
And there's no imminent benefit to just go and try to convert all SAP HANA live content to CDS now just for the sake of it.
Concerning performance: CDS is not a new execution engine in SAP HANA. All queries against CDS views are internally transformed into a query structure that could have been a SQL query and then handled just like any other query.
So, all the execution engines you mentioned are still available for queries against CDS tables and views. You can even use CDS views in calculation views and that still would work.
And of course you can use the same set of query analysis tools for CDS views as you can for "normal" views.
Hope that clarifies a few points.