Using alias targets in CMake

When defining CMake targets one can create alias targets so that the alias name can be used to refer to the defined target in subsequent commands. For instance

add_library(foo_lib foo.cpp bar.cpp bat.cpp)
add_library(foo::lib ALIAS foo_lib)

As far as I understood it, this has the advantage that the name foo_lib doens't appear as a make target. However, given such an alias name I'd like to set all kinds of properties to them such as:

set_target_properties(foo::lib PROPERTIES COMPILE_DEFINITIONS ...)
target_include_directories(foo::lib PUBLIC ... PRIVATE ...)

but this is not possible unfortunately, since CMake Error: set_target_properties can not be used on an ALIAS target. I don't see why this shouldn't be possible as I'd like to define the name of my lib once and refer to the given alias whenever I want to adjust a property of the target. Any hints on how to use ALIAS targets "correctly"? What is the purpose of ALIAS targets other than they're not appearing as Make targets then?

ALIAS similar to "synonym". ALIAS target is just another name for original one. So the requirement for ALIAS target to be non-modifiable - you cannot adjust its properties, install it, etc.

One of possible scenario for creating alias - having target, which conceptionally differ from original one, but effectively the same (e.g., in given configuration):

if(FOO_USE_SHIPPED)
    add_library(FOO ...) # Library FOO shipped with our project
endif()

...

# We need FOO_test for testing
if(FOO_USE_SHIPPED)
    add_library(FOO_test ALIAS FOO) # Use our library
else()
    add_library(FOO_test IMPORTED)
    set_target_property(FOO_test ...) # Use external library
endif()