Of course, you should just report the structure of the model and state that no parameter is significant.*

Reducing the model by removing some factors would be a kind of p-hacking.

You could certainly make some sensitivity analysis (i.e.: simulations with known effects) to see what effects would have been recognizable with your sample size under what conditions. If these effects are large enough to be relevant, you may conclude that your study is unlikely to having missed some relevant effect.

*The report also includes an explanation of the rational of the model and the plausibility of the model assumptions (which also includes a reasonably detailed description of how the data were obtained).

could there be an interaction effect, having influence on the results

If it's a somewhat confirmatory analysis that is supposed to summarise the results of your experiment or so, I completely agree with Jochen Wilhelm . You couldn't just write it up and try to find an explanation for your findings, could you?

Then again, I feel that in my discipline hardly any conceptual model I know of is developed in a way that there would be a one-to-one relation to statistical modelling. (You might argue that this is very unlikely if not impossible if latent constructs come into play.) So more often than not there would be at least a few different (statistical) models that equally make sense (from a conceptual perspective).

Now I don't know about your discipline, but If I take your comment literally, and ALL the coefficients in your model are estimated to be somewhat zero, so are the variance components :-)

In this (some of my colleagues would argue: in any) case a simplified model (e.g., no random slopes, a marginal model, ...) could be something worthwile investigating ...