Are you sure the figure is actually just their salary? If it has been taken from the taxpayers alliance report, the figure includes pension contributions and payment of out of pocket expenses and benefits such as lease car etc. It might also include payment for other duties such as Returning Officer. For some councils the figures recorded were actually redundancy payments paid out in that year.
When considering whether you think they are worth that level of pay, think about:
how many staff do they employ? For many councils, it can be thousands.
the size of budget they control. This could be millions.
the services the chief executive is responsible for and the importance of those services (e.g social services, education, highways). Is the chief executive legally culpable when things go wrong?
the complexity of running a large organisation with such diverse services (hard to think of a private company that runs such a range of services)
the complexity of working with councillors, paid staff, the general public and having to have a public profile.
the experience and skills of the person.
It is a very stressful job and not one that you can ever totally switch off from. The buck stops with the chief executive.