The manual tells you why.
Quote:
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The pan should not be more than one inch larger than the burner grate. The maximum pan size is a 10-inch skillet. Oversized cookware will cause excessive heat build-up in the stove top and will result in damage to the burner grate, burner and cooktop
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If you have a lot of overlap such as with excessively large pans or griddles that cover multiple burners, you have a lot more surface reflecting heat back to the stove and it is possible, given time and a few other things lined up just right, to get the stove hotter than it was designed to handle.
You do need to keep in mind that the manual is a 'best practice' guide with liability concerns in mind for a suit happy consumer market.
Also keep in mind that best results means using the right tool for the job. An RV stove is not intended nor designed for commercial grade or mass feeding cooking. It is size and weight (and energy) constrained and in an environment where occasional use and 2-4 person dinners are the norm.
If you've got mass feeding as your need, then you should get the right tools for that job. That means upgrading from 5 kBTU/hr burners to 30k or more, using the equipment outside an RV or other confined space so combustion products and water vapor are not issues, and so on.