It is absolutely the case that serving at the pleasure of a minister is troublesome for any head of a major policing or security organization. It's not necessarily that the commissioner lacks the integrity or the personal ability to stand up to their minister. It's simply on the point that they will tend, over time, to manage with one eye upwards, as they call it, in the sense that they have to anticipate the wants and desires of the minister, sometimes against the interests of their organization.
The RCMP is the best example that exists of how that model is troublesome. If there wasn't a sort of tripartite arrangement but there was at least a very transparent and clear information exchange, then if the commissioner were to be dismissed on questionable grounds, at least there would be public awareness and potentially outrage for an egregious dismissal.