There's no need to raise the cap and all the Apples and Googles get all the applicants they want. Today the majority of H1-B visas go to Wipro and Infosys and the like for low paid tech grunts; Apple won't have any trouble outbidding them. And those tech grunt companies aren't doing anything valuable for the USA so it won't be any loss to have them struggle.
In fact, we should be able to drop the cap to a more reasonable 30-40,000 instead of the recent 85,000.
And we should be able to eliminate almost all the paperwork. In the current system, a US government bureaucrat tries to determine if you're qualified when you apply. Applicants hire lawyers to fake, translate, fabricate, apostille, and make up education and work experience that USCIS expects. If applicants are paying cash, we can presume they're qualified and reduce the application paperwork to one page.