The simplest lever available
When results deteriorate, a club has relatively few immediate levers it can pull. Rebuilding a squad takes transfer windows and significant money; changing a whole club's structure takes years. Removing a single individual, by contrast, can be done within days and is the most concentrated, quickly executable decision available to a board under pressure. This practical asymmetry, rather than any settled belief that the manager is always primarily responsible for poor results, is a large part of why managerial change is so often the first response to a bad run of form across the sport.
A signal as much as a solution
Beyond its direct effect on performance, sacking a manager sends a visible signal to supporters and shareholders that the club has recognised a problem and acted on it, which carries value independent of whether the change actually improves results. This is one reason clubs sometimes make managerial changes even when the underlying cause of poor form, such as an ageing squad or a lack of investment, is unlikely to be solved by a new appointment at all, since the decision is partly about visibly demonstrating accountability rather than purely about the football itself.
The mixed evidence on whether it works
Studies looking at results before and after managerial changes across leagues tend to find a temporary uplift immediately following an appointment, often attributed to a short-term change in effort and freshness among players, but a less clear long-term improvement once that initial bounce fades. This suggests managerial change functions partly as a reset rather than a guaranteed structural fix, and it is a useful reason to treat any short run of improved results after a new appointment with some caution before concluding that the underlying problems have actually been resolved.