This would of course drive towards commoditization of grading services, which is a disincentive to providing grading as a service to begin with. Look at coins (PGCS and NGC) or sports cards (PSA, CSG, BGC). While they all use a 10, 70, or 100 point scale, they compete now only on speed of service and innovations in their respective product holders (and a few other added services like photos), and by casting shade on each other.
People still argue whether a PSA 10 is better than a Beckett 9.5 for example, or whether something is MS-63 or -64. You wind up in the same place.
There are only three expertizing agencies that I am aware of that grade stamps, PF, PSE and PSAG. Ironically the last, PSAG, was at the forefront of grading but is now an also ran based upon what you see in auction and retail sales. Crowe also offers the service but is not anywhere near the main three organizations size.
All three have as their main business certification of authenticity and along with those opinions come analysis/ examinations for faults and assorted chicanery.
The three already have their proponents and detractors, often tied to exactly what item it is that you seek an opinion upon. I have seen little evidence of "shopping" between the three for a higher grade and my experience shows much uniformity between PSE and the PF grades.
My opinion is that where an item is sent has little to do with what grade you think you might get from one organization or the other but rather how much you trust their expertizing. And since you cannot get a grade without first getting the expertizing service having a standard for grading would not have a negative impact on the industry.