Eventually they should let in immigrants, but maybe it is worth waiting until the shortage has managed to work its way through the system and cause some real improvement to working conditions for Americans.

As a Nordic who has lived in the US, I got to say American put up with some really shitty working conditions. In the Nordics we developed good conditions over time by having something like 80% of the population in unions which even created national federation. That gave a lot of bargaining power that made sure workers got good conditions.

An I mean conditions and not merely salary. Very often that bargaining power has been used to imrpove access to vacation, sick leave, letting workers have some say at work etc. Thus stuff matters. When COVID19 hit the US, it went like wild fire through American meatpacking plants where poorly paid workers had been basically packed on top of each other. Why did that not happen in a northern European countries such as Nordics and Germany? Because thanks to large strong unions, workers never worked under such conditions, with that kind of cramped spaces and poor ventilation.

The US may not have much of unions, but now the market is able to do what unions have not been able to do for decades in the US, which is to force an improvement in working conditions. Naturally first priority for people has been a more decent wage. But workers also need more favorable conditions for sick leave, vacation, health care etc.

Opening the flood gates for immigration today, would kill a once-in-a-lifetime opportunity to push through better conditions.

Immigration is a two-edged sword. It gives new opportunities for poor people and often it can improve the overall economy, but it can also lead to lower standards. The beginning of the American industrial revolution saw working conditions which were not too bad. As soon as poor immigrants started flooding in from Europe, working conditions collapsed.