We only have projects with low risk
A risk analysis performed in the early stage of a project will most likely conclude that the project risks are not significant. Otherwise, if this is not the case, the project may not be started at all.
The initial analysis will probably list a set of risk controls for mitigating the identified risks, so that an acceptable risk level is achieved.
The thing that is not evident from the initial analysis, is that during the course of the project the World changes, and the assumptions of the analysis no longer holds true.
Steering a project from beginning to end based only on initial assumptions is a recipe for project failure. Using an outdated risk analysis may be worse than not having made the analysis in the first place.
A project risk analysis should ideally be updated each time the project or any of the assumptions changes. This task is the central part of a continuous risk management process.
With a periodically updated analysis, it may much sooner come to the project management's attention, if the project is going off track on budget, time or quality.