That would penalize startups, giving only large companies access to the foreign labour pool. It's rare that a problem like this has a simple solution.
Plus it usually takes 2-3 years to know if someone isn't going to get the H1B lottery during their OPT which is a longer time horizon than most startups are concerned with anyways.
I think most startups simply hire who they view as the most qualified person regardless of immigration status.
Source: Have a startup that hires software developers.
The problem with using sweeping statements like "anyone who can..." is that one example is enough to disprove you. There'll be Who's Hiring thread in a couple of days, watch how many young startups say no new H1Bs on that.
Your OPT case is only true when hiring a student on F1
We don't have to wait - we can look at the one from last month: https://news.ycombinator.com/item?id=15384262
I did a Ctrl+F and nothing came up for "H1B" and the only thing that came up for "citizen" was a job posting for the US government itself.
Edit: I had to get to page3, but: https://news.ycombinator.com/item?id=15391862
https://news.ycombinator.com/item?id=15386201
(Though I believe the second one is some team specific thing, I know that at least AWS sponsor H1Bs for fresh grads).
Then on p5: https://news.ycombinator.com/item?id=15384311
(I was confident about this because I was job hunting about a year ago, and was exclusively looking at companies under 50 people. Most of them were fine with H1B transfer, but explicitly said no new applications.)
If they hire someone who already has an H1B working at another company they only have to perform a transfer, which is processed as a lottery-exempt new application i.e. same salary and credential and experience requirements as a new application but no need to go through the lottery. Most startups likely aren't going to hire someone fresh out of school or straight from another country (hence needing a new, lottery H1B). They will prefer someone who is local and has some experience.
> Plus, the application is just beyond what most startups are going to have the time to do.
H1B transfers take 15 days if premium processed, which is an additional fee of ~$1500. That's well within the budget of your average VC-funded startup. The transfer also adds an extra 2 weeks to an H1B candidate's start date over a domestic candidate (because no candidate is going to give 2-week notice at their current job until the transfer is approved) but it's not an insurmountable issue.
It's true that super-early stage startups (< 20 employees) may still not bother with this extra bureaucracy. But there I think it's because at that size the founders' and early employees' professional networks provide a sufficiently healthy pipeline of candidates, so they'd rather keep working and shipping than deal with immigration lawyers. On the other hand if someone on the founding team isn't a citizen/permanent resident, they'd still do it (eg. Laks Srini at Zenefits).
The startup doesn't need to file the H1B themselves. The employee can transfer it from another company.