They could. This is the way most early implementations of templates
worked, and is still the way the Microsoft compiler worked. It was felt
(in the committee) that this was too error prone; it made it too easy to
accidentally hijack a name, with the instantiation in one translation
unit picking up a local name, rather than the desired global symbol. (A
typical translation unit will consist of a sequence of #includes,
declaring the names that everyone should see, followed by implementation
code. At the point of instantiation, everything preceding the point of
instantation is visible, including implementation code.)
The final decision was to classify the symbols in a template into two
categories: dependent and non-dependent, and to insist that the
non-dependent symbols be resolved at the point of definition of the
template, to reduce the risk of them accidentally being bound to some
local implementation symbols. Coupled with the requirement to specify
typename and template when appropriate for dependent symbols, this
also allows parsing and some error checking at the point of definition
of the template, rather than only when the template is instantiated.