In your case I would be hugely suspicious of what the Head did! Leaving so soon is odd. Obviously her exit strategy was lined up.
Recruitment can be hard. Schools on national conditions give salaries within bands depending on size of school. Heads of medium sized schools should get L8 minimum. It goes up to L21. More if school
is bigger and Group 3. You don’t have to appoint on the bottom either. You pay according to the skills your new head has and obviously previous salary.
Number of applicants is besides the point. Three (or even 2) great ones is better than 6 average ones. Yes. The mat left it too late but they can take action to cover the post.
However there are huge downsides to not having a head. Deputy doesn’t want to be a head so they won’t drive anything forward. Probably lack the skills anyway. It’s not really lonely being a head. It’s collaborative, especially with SLT and senior teachers. However you make decisions. Deputies who don’t want to be heads usually will just allow the school to coast. Are they interpreting assessment data, amending the improvement plan, gathering evidence, planning training, and everything else that’s required? Possibly not.
Most schools really don’t have lots of angry parents. This isn’t a big part of the job. Clarity of vision, getting the best teachers and keeping them and meeting targets is vital. Lots of data analysis. Heads need a SLT on board with their vision and the GB.
They do get holidays. They just don’t have the same contract as teachers and directed time. Most take a big chunk in the summer but some don’t. Depends on the school and circumstances. Heads trying to improve schools work very hard. Others can afford to coast a bit occasionally. You cannot make people do the job. MATs have not made it any more attractive. But for some it’s a dream job. I’ve met many who think it is and thrive. We need to federate smaller schools more under one head and pay more. This helps a lot. No one needs 3 heads for 3 close village schools for example. Get one and pay more.