Why are pip packages not installed to $PATH to by default?
You're confusing $PATH and $PYTHONPATH. site-packages is for libraries,  $PATH is for programs (binaries and scripts). pip installs libraries into its site-packages and scripts to the corresponding bin/ directory; e.g. if site-packages is /usr/local/lib/pythonX.Y/site-packages scripts are installed into /usr/local/bin/.
pip doesn't check if /usr/local/bin/is in $PATH. Well, I agree with you — it should check and remind user to add bin/ directory to $PATH if it's not already there.
Typically when using rubygems in the ruby ecosystem or npm/yarn in the JavaScript ecosystem packages are installed somewhere on the $PATH or at least you are instructed to add the package install location to your path $PATH.
It seems like with pip in the python ecosystem there is never an emphasis on this. Instead, you are encouraged to run modules via python -m <name>, etc.
Seems a bit odd to me, was this just a design decision? Is it good practice to put site-packages or whatever location pip is using into $PATH? Sometimes a binary is added to /usr/local/bin (and sometimes with a different name than the package itself e.g django-admin instead of django with pip install Django whereas the binary is usually the same as the package name in ruby/JavaScript ecosystems), for example, I see, but is that all of the time?