I once heard someone describe compression programs as 'expansion programs with interesting failure cases', and so, of course, the best compression program to use depends on exactly which failure cases you're interested in.
However, PAQ tends to be really* slow, largely because it tries more things. It's highly tunable, but people who aren't compression geeks tend to not want to tune their compression. Presets are available.
That's pretty much why it hasn't caught on - speed. There may be some hybrid approaches that deliver a better compromise between context mixing's effectiveness and dictionary coding's speed and memory usage: I guess you could argue LZMA, bringing a Markov-chain algorithm into the mix, is one such, in a way. Sort of.
I'm also a little antsy about ZPAQ formats containing bytecode descriptions of the decompression algorithm needed, and are, broadly speaking, executable (and in some cases, are). That seems like the kind of thing that may invite security problems if approached without due caution.