Is there a code article I can site that requires replacement of corroded switchboard enclosures (bottom completely rusted away)? 110.7 Wiring integrity?
Not really, though it may affect what you do replace it with.
NEC isn't really that much about evaluating what is existing for the purpose of determining if it is safe to continue to use, but such conditions do help set a floor for how corrosive the area may be when it comes to selecting new equipment.
Now depending on circumstances simply drilling weep holes in what was there could possibly have impacted how long it lasts if the reason for corroding away was mostly due to condensation buildup and not because of high amounts of corrosive agents.
The path forward seems obvious to me, it is time to remove and replace, but, not to the owner. The entire bottom of the switchboard(s) and disconnects are missing due to corrosion. Looks like years of neglect and possible flood damage along with close proximity to salt water.
NEC is an installation code not a maintenance code.
The fact the bottom rusted out doesn't mean any NEC code was violated, just that determining conditions of the application may not have been what designer had expected.
What did the customer call you to do? I’ve gotten tired of arguing with people about unsafe equipment. If I don’t need to go into the equipment, let them keep as is and take the risk.
Is there a code article I can site that requires replacement of corroded switchboard enclosures (bottom completely rusted away)? 110.7 Wiring integrity?
The original installation should have complied with 110.3(A)(1) and 110.11. The question is if it didn't comply initially does it now need to be replaced?