Why are appraisals not portable from bank to bank?

[Johann Jells]

As I understand the law today, banks must get an appraiser from a pool rather than choosing one, so there's a firewall that there wasn't in the past. So why am I told that one bank won't accept the appraisal commissioned by another? It seem all this accomplishes is "lock in" to the 1st bank unless you want to eat the cost of another appraisal. It seems very consumer unfriendly in an era where these kinds of loans are heavily regulated and more or less a commodity product.

I have an appraisal scheduled for tomorrow for a cashout refi on a 3 family investment rental that they were only willing to lend 70%. I'm having 2nd thoughts and think I will delay to shop for a 75% that will be more likely to let me eliminate the 6.5% loan on another property.