Why wouldn't customer cars work and didn't they used to be part of F1 as the norm?
@toomanyarmies, via Twitter
In the past, customer cars were the norm but usually they were at least one-year-old cars being run by teams that were not quite as professional as those that built them. Often, they had 'gentleman drivers' to foot the bills.
Customer cars would work but the biggest problem is that to build a Ferrari F1 car probably costs at least twice what it costs Sauber to build its cars. With the greatest respect to Sauber, it would struggle to get the performance out of it that Ferrari gets out of its own chassis, so I don't think it would improve overall either financially or competitively.