(I guess I could be called a member of one of the teams ;-) this is my view)
I thought of staying out of this debate, but perhaps some words of clarification or, let's say, some thoughts are in order after all.
LaTeX3 versus pure Lua
First of all this is the wrong question imho: LaTeX3 has different goals to LuaTeX and those goals may well be still a defunct pipe dream, but if so they are unlikely to be resolved by pure Lua either.
So if one wants to develop an argument along those lines then it should be more like "Why does LaTeX3 use an underlying programming language based on eTeX and not on LuaTeX where a lot of functionality would be available in a "simpler" way?"
But LaTeX3 is really about three to four different levels
- underlying engine
- programming level
- typesetting element layer
- designer interface foundation layer
- document representation layer
See for example my talk at TUG 2011: http://www.latex-project.org/papers/
Here is a sketch of the architecture structure:
The chosen underlying engine (at the moment is any TeX engine with e-TeX extension). The programming level is what we call "expl3" and that is what I guess you are referring to if you say "LaTeX3" (and I sometimes do that too). However, it is only the bottom box in the above diagram. The more interesting parts are those that are above the programming level (and largely a pipe dream but moving nicely along now that the foundation on the programming level is stable). And for this part there is no comparison against Lua.
Why use LaTeX3 programming over Lua, when LuaTeX is available?
To build the upper layers it is extremely important to have a stable underlying base. As @egreg mentioned in chat: compare the package situation in 2.09 to the package situation in 2e. The moment there were standard protocols to build and interface packages the productivity increased a lot. However, the underlying programming level in 2e was and is still a mess which made a lot of things very complicated and often impossible to do in a reliable manner. Thus the need for a better underlying programming layer.
However, that programming layer is build on eTeX not because eTeX is the superior engine (it is compared to TeX but not with respect to other extensions, be it Lua or some other engine) but because it is a stable base available everywhere.
So eTeX + expl3 is a programming layer that the LaTeX3 team can rely on of not being further developed and changed (other than by us). It is also a base that is immediately available to everybody in the TeX world with the same level of functionality as all engines in use are implementing eTeX extensions.
Any larger level of modifications/improvements in the underlying engine is a hindrance to build the upper layers. True, some things may not work and some things may be more complicated to solve but the tasks we are looking at (well I am) the majority are very much independent of that layer anyway.
To make a few examples:
good algorithms for automatically doing complex page layout aren't there (as algorithms) so Lua will not help you here unless somebody comes up with such algorithms first.
something like "coffins", is thinking about approaching "design" and the importance here is how to think about it, not how to implement it (that comes second) -- see Is there no easier way to float objects and set margins? or LaTeX3 and pauper's coffins for examples
Having said that, the moment LuaTeX would be stable similar to eTeX (or a subset of LuaTeX at least) there might well good reasons for replacing the underlying engine and the program layer implementation. But it is not the focus (for now).
Why use LaTeX3 to program at all? Why not turn its development into the development of a LaTeX-style document design library for LuaTeX, written in Lua?
Could happen. But only if that "LuaTeX" would no longer be a moving target (because LaTeX3 on top would be moving target enough).
Side remark: @PatrickGundlach in his answer speculated that this
answer that the LaTeX3 goal is backwards compatibility. Wrong. The
same people that are coming down on you very strong about
compatibility for LaTeX2e have a different mindset here. We do not
believe that the interesting open questions that couldn't get resolved
for 2e could be resolved in any form or shape with LaTeX3 in a
document-compatible manner.
Input compatible: probably. But output compatibility for old
documents, no chance if you want to get anything right.
But in any case, this is not an argument for or against implementing the ideas we are working on one day with a LuaTeX engine.
Is the separation of LuaTeX and LaTeX3 a result (or at least an artifact) of the non-communication among developers that Ahmed Musa described in his comment to this answer? What kind of cooperation is there between these two projects to reduce duplication of effort?
As I tried to explain, there is not much overlap in the first place. There is much more overlap in conceptual ideas on the level ConTeXt viz. LaTeX.
An even more fantastical notion is to implement every primitive, except \directlua itself, in terms of Lua and various internal typesetting parameters, thus completely divorcing the programming side of TeX from the typesetting side.
That brings us to a completely different level of discussion, namely is based on LuaTeX, or anything else for that matter, a completely different approach to a typesetting engine possible? That is a very interesting thought, but as @Patrick explained it isn't done with leaving TeX to do the typesetting and do everything else in a different language. So far such concepts have failed whether it was NTS or anything else because fundamentally (in my believe) we haven't yet grasped how to come up with a successful and different model for the TeX macro approach (as ugly as it might look in places).
Best Answer
The LuaTeX developers have commented on their choice of Lua over other languages, including Python, on their home page.
Embedding the interpreter is one thing, and apparently no fun with Python. Another is to actually make the innards of TeX visible to the embedded interpreter. While much of the communication code could likely be adapted in some way from LuaTeX to PythonTeX, it will still be a lot of work.
A better approach may be to cheat a bit, and simply piggyback on the LuaTeX interpreter. There is a bridge that 'embeds' Python inside Lua called Lunatic Python, and maybe it can be made to work with LuaTeX also. However, it may be easier to just use XML-RPC: Let LuaTeX spawn a Python process, which acts as the XML-RPC server. LuaTeX commands can then make calls to the Python process. Bonus feature: Once this is implemented on the LuaTeX side, it can be used with any other scripting language, not just Python.