In this context, I believe that your report card is your completion of certain content. It varies from person to person in terms of what they want to do/play, but all a parser gives you is a number, it doesn't tell you how good of a player you are or how well you play the job and/or role you have. The most it can tell you is that in the specific conditions of the fight you parse, you executed your rotation with X% efficiency. It doesn't tell you how well you avoided avoidable damage, it doesn't tell you how well you did with a mechanic, or how well you did picking up or shedding adds, it doesn't tell you whether or not you were aware enough to see that one of your team mates needed help and you drew an enemy from them to help, etc, etc... All it is is a number. It falls very far short of helping you or anyone else actually get better at their job or role. It can give you bare numbers, but no nuance.
An experienced driver can tell from the gear they are in and the pitch of the engine what their speed is, they can feel the car move and know if they have good traction, and a really good driver can tell simply by looking through the windshield roughly how fast they are going. Having a speedometer doesn't teach you how to drive, how to steer, brake, park, etc. Your speedometer doesn't teach you lane awareness, or to look in your mirrors, it doesn't navigate for you, or handle stop signs and traffic lights. Your speedometer can't teach cadence braking, or steering into a skid, how to handle ice or hydro-planing. A speedometer can be a useful tool, but it's a limited tool, and really not a major part of being a good driver. So, your analogy fails.
By all means people should improve their play, but a parser, damage meter, or log analysis or whatever other method can only tell you about one facet of what you need to do - damage output.
Similar to telling your mates at the pub that you got your Mustang up to 100 mph on the Motorway/Interstate/Autobahn. Ego inflation, bragging and telling your friends that they need to do the same in their cars...aka 'git gud'. Yep, you called it, absolutely.