Same thing goes for climbing. There are multiple grading systems used around the world, but whether someone uses one or another doesn't change the properties of the climb itself. The grading systems are just a shorthand interface for the climbing community to reference (which indexes difficulty, expected types of holds/distances between/traverses/techniques to be employed/angles of pitch etc).
However, what does change is reference points (just like in martial arts) as someone increases in capability. If someone rises to become an Intermediate climber (someone who comfortably climbs V4s and tops out at V6s in the V-scale) a V2 is going to be a trivial problem to surmount relative to a Beginner climber. Same goes for a high-end Advanced climber who will now look at V4s and V5s much like the Intermediate climber looks at V1, V2s, and some 3s; trivial to surmount.
The features of the climb to surmount don't objectively change in a material since when interacted with whether you're using the V-scale or the Font scale (where a V6 might be a 7a). What does change are the reference points to the obstacles as climbers increase or decrease in various aspects of climbing facility.
These reference points as facility increases/decreases are what generates "mook-gating" whether it be AD&D or D&D 4e (where both systems reference an assigned statistical value of one thing - HD of HP value of monsters - against an assigned statistical quality of another thing - Fighter/Ranger/Paladin/hero or adventurer status).
Climbing is neither more nor less immersive because of the diversity of grade-scaling as a reference point and that diversity of grade-scaling doesn't decrease a user's ability to build out a working mental model of a route/obstacle and their prospective ability to surmount it (both before a prospective climb and during it).