It's not that you can't initialize signs--it's just not necessary to do it, especially with unambiguous signs. In the case of "pahk-the-cah", the vehicle classifier in the palm is very clear, so there is no need to initialize it for further differentiation.
In educational settings, more initializing is sometimes used to connect signs to specific words rather than concepts. That's similar to the whats happening to spoken words overseas. For example, a French person making an English word "French" by sticking a "la" or "le" in front of it. It's not really a French word but an English word that has been adapted fit to their language. Many French people resent that because they feel that is an illegitimate tampering of their native tongue. But it is an accommodation many French people make, especially with modern technological and lifestyle terms.