Actually the goal of terms like that is efficiency. We could say "supporter of aggressively implemented authoritarian communism" if we wanted, but tankie is shorter.
Helps if you have the background to understand the specifics of what different "isms" support and thus what they disagree on that leads them into genuinely fighting each other. A fascist, a lib and a tankie really do have very core disagreements that cannot be realistically compromised on. At the most basic, a fascist wants a unified society with a strict hierarchy, the tankie wants a unified society with no hierarchy, the lib doesn't want any kind of unified society. If any one of these people gets their way, the other two do not, which leads to conflict.
Left/right are more economic arguments with some wiggle room due to being more or less a spectrum, but also tend to feature significant real world disagreements.
Anyways, I do agree that it's important to have conversations about these underlying details, but when you're talking amongst other people who know the background already, some shorthand terms are going to start appearing. Since these are overarching governance philosophies that any person can adopt or discard at will, they're also a little different from more inherent divisions, like ethnicity for instance. Being a tankie, lib or fascist is a choice, where being Arabic or gay or something is not.