Why don't we have the capacity? Well the complete lack of coordination and leadership at the federal level means that each individual entity, whether it be state level government or a private entity, is having to do everything from scratch. That means developing SOPs, procuring supplies, and validating both the processes and reagents. This is being done on emergency orders as well, so some of the standards are relaxed to quickly get things up and running.
There's also a shortage of reagents and kits because we didn't have or need this testing just a few months ago. There's also international competition for these resources, and because the US has decided it doesn't want to actually work with or coordinate with other countries, it's a free for all.
Because everyone's frantically working on the same thing, but looking out for themselves it also means that true high throughput solutions are slow to develop as well.
I could go on and on, but it's a clusterfuck and no one at the federal level either A) seems to care or B) thinks that it's their responsibility.
Source: wife is currently in charge of starting up Covid testing