Why is it OK to bond the neutral and ground in an appliance?
That is absolutely correct.  It is not OK to tie neutral and ground of an appliance.  This is literally bootlegging ground.  

"Ok" is not the same thing as "legal".  It is legal to do this, only on dryers and oven/range, when installing on old wiring with no ground. This was a compromise worked out with the appliance industry, who feared losing sales.  The rationalization is that dryers and ranges are rarely unplugged and moved, so a neutral wire failure is unlikely.   

Unrelated, since then, Code now broadly allows retrofitting grounds. 

Hooking up an appliance in this regime

There are only two legal ways to connect a range or dryer. 


using a 3-wire connection (hot-hot-neutral no ground), you are to bond neutral to ground in the range or dryer. 
using a 4- wire connection (hot-hot-neutral-ground), DO NOT bond neutral to ground in the range or dryer.  This bond should be removed. 


Using a 4-wire connection and still bonding neutral and ground would be a disaster for the reasons you cite.