Section 12.5 from Templates the Complete Guide (Amazon) contains this quote:
You may legitimately wonder why only class templates can be partially specialized. The reasons are mostly historical.
It is probably possible to define the same mechanism for function templates (see Chapter 13).In some ways the
effect of overloading function templates is similar, but there are also some subtle differences. These differences are
mostly related to the fact that the primary template needs to be
looked up when a use is encountered. The specializations are
considered only afterward, to determine which implementation should be
used.In contrast, all overloaded function templates must be brought
into an overload set by looking them up, and they may come from
different namespaces or classes. This increases the likelihood of
unintentionally overloading a template name somewhat.Conversely, it
is also imaginable to allow a form of overloading of class templates.
Here is an example:// invalid overloading of class templates template<typename T1, typename T2> class Pair; template<int N1, int N2> class Pair;However, there doesn’t seem to be a pressing need for
such a mechanism.
Furthermore, the Design and Evolution of C++ (Amazon) contains this quote in section 15.10.3
I therefore concluded that we needed a mechanism for “specializing”
templates. This could be done either by accepting general overloading
or by some more specific mechanism. I chose a specific mechanism
because I thought I was primarily addressing irregularities caused by
irregularities in C and because suggestions of overloading invariably
creates a howl of protests. I was trying to be cautious and
conservative; I now consider that a mistake. Specialization as
originally defined was a restricted and anomalous form of overloading
that fitted poorly with the rest of the language.
Bold emphasis mine. I interpret this as saying that function overload resolution is more difficult to implement (and get right by users) than class specialization. So probably no real technical obstacles (similary for function template partial specialization) but an historical accident.