> A secondary reason with closed systems in particular is that it may reveal methods it uses which is a competitive advantage to other systems.

I doubt this is the case. Mathematica at least doesn't really contain any "magic" in the actual algorithms and uses pretty well-known methods that are for the most part documented, if not open-source. Most of their competitive advantage is in the design of the language itself, the interface and in their internal virtual machine. These details aren't really things you would get any insight into with a "show the work" mode.

Your first reason is totally right though. "Show the work" mode requires a lot of extra stuff, because the way a person reasons through solving some thing like an integral isn't much like how a computer solves it. To make it spit out something really comprehensible to a person, you have to have lots of heuristics and it isn't generally very reliable. Even automated theorem provers (which Mathematica has some very basic functionality for) spit out rather hard to follow or extremely long proofs. Those are much more rigorous and less reliant on heuristics than a CAS and still don't produce "pretty" output (AFAIK, I'm not super experienced using automated provers or proof assistants).

Showing steps has been done before, e.g. by Macsyma like OP mentioned and by Wolfram too (Alpha does it). It's just not that great for problems of any substantial complexity.

You could feed the proof to a (simple, verified) proof checker rather than check it by hand. Then you only need to check the statement that was proven was the one you wanted, without having to vet the code that spits out the proof line by line (until you actually hit a bug and the proof fails to check). I don't think it would be inconceivable for mathematica to implement something like that, though perhaps it's not really their core business.

I really would like to be able to see a proof of how Mathematica calculates a limit, for example. Doesn't need to be human friendly, just verifiable.