The data I saw when they were making decisions for californias plan (January?) was something like first dose was 65% effective (at no symptoms, there were no hospitalizations reported after one shot) and the second dose took you up to 95%. As a public health measure, getting one shot in twice the people is far more effective. You limit the spread substantially and drastically drop the hospital beds required. I'm not sure if information further to that changes anything. If that is still true, as a public health measure, 2nd shots shouldn't start until all the first shots are in. Some exceptions for people highly exposed (eg ICU/LTC staff) makes sense to protect individuals (and by extension the viability of the healthcare system).
California chose to give most people one shot using the above logic. Again, not sure if that has changed.
@Delboy likely knows more.
I think Ontario is operating on a similar strategy and gov't doesn't have the stones to say it. They are trying to get most people one shot (other than healthcare workers and LTC residents) and then giving out 2nd shots to placate people that two shots were required as per the manufacturer.