As someone who got "rejected" in the H1B random lottery - yes, the system needs an overhaul. Perhaps an auction system would be appropriate, where companies bid on visas, then top N bidders get visas from the pool, paying the lowest winning price. This would also work well with the idea that companies should first seek talent within the United States. The auction final quote would be a clear, publicly available portion of the costs of getting employees abroad. The only caveat I see is potential employment contract clauses forcing employees to stay in the company for a certain number of years. Currently there are no restrictions for switching jobs on an H1B.
Where N becomes a political football that us raised and lowered at the whim of lobbyists ultimately allowing wages to fall below market rates.
There is no labor shortage in a nation of 300 million with the best university system in the history of humanity.
If we need any sort of system, the appropriate one would be to reward companies that train citizens in skills the employer needs in order to fill any sort of skills gap.
While in principle I agree with you, in practice N was most of the time equal to 65k, with the exception of the dot-com bubble (years 1999-2003, so 80% of the time; program was added in 1990). And there probably should be something like H1B in any immigration system. Anyhow, the current political climate in the US does not give many hopes for an upgrade. In the meantime, I've discovered Switzerland, and quite honestly - I'm not looking back.
I'd rather just eliminate the H-1B (and some other classes of visa) entirely, and just add a new blanket supernumerary visa that works like this:
(1) There's a fixed initial fee and an annual renewal fee for it,
(2) Anyone who doesn't have any of the features which exclude you from immigration regardless of qualification in other categories can apply,
(3) The visa category is issued without numerical limit to qualified applicants,
(4) The visa is a dual-intent non-immigrant visa (that is, you are not prohibited from applying for an immigrant visa, if you are otherwise qualified for one, while present on it),
(5) The visa does permit you to work without restriction while present on it.
I think it's not unreasonable to have an auction system in place. You don't want your labor market to be suddenly flooded by foreign workers - this isn't to say that they're bad, but when it's a singular large number in proportion to the existing workforce, it can be very disruptive short-term.
This doesn't necessarily have to come with a hard cap - you can just increase the bar slightly for every new application that is filed, and let the market figure out where the profitability bar is.