It's a false premise that startups are currently competing against large companies like Microsoft for H-1B visas.

The biggest H-1B users are offshoring/outsourcing companies (source: http://www.nytimes.com/interactive/2015/11/06/us/outsourcing...)

Moving to an auction system will in fact improve a startup's chances - most VC funded startups can comfortably outbid an outsourcing company. The outsourcers' business models are dependent on visa costs being on the low side.