I really like your suggestion. Sadly, it didn't work for me. My email address was once associated with a small company (that my wife and I ran). So Google considers it to be a commercial address, and wants $10/month for a Google Voice number.
Chickens and eggs: I want a new Google account, for which I need a new phone number. But to get a new phone number, I need a different Google account.
Is the discussion of "load balancers for resilience vs scale" even relevant in a cloud-enabled world? Just use an AWS Elastic Load Balancer with an Auto Scale Group, plus Cloudwatch alarms for monitoring and you get the best of all worlds... :-)