The material point about the nightingale hospitals was that except in very specific circumstances where there was already a significant shortage of beds, they were not the solution the NHS itself had been involved in making, wanted, could staff or could see the logic in. It was a headline grabber for the government in the darkest times, aimed at reducing anxiety in the population.
Most nightingale hospitals weren’t needed, because most hospital systems have empty beds, which were recommissioned, and provided care in a safe environment. Staffing was a massive problem, but at least within the hospitals staff could be identified to work extra hours, moved from one role to another etc. very much like the vaccination programme in fact. We have a huge amount to thank the NHS for.