Much of the problem comes from the fact that there is insufficient incentive for the studies to be effective in the first place. The sample size issue is real and often justified due to a lack of resources, but this results in minimum publishable units which are anecdotal and an over-reliance on meta-studies which attempt to aggregate these positively-biased results. Increasing the sample size is not always possible, but sometimes there are alternative trial designs which can yield different but more reliable outcomes.

Another aspect of effectiveness comes from whether the animal studies are actually designed to advance anything at all. For example, if the goal is to develop an imaging technique in humans, then the purpose of animal experiments is primarily to confirm that the idea is not wrong, debug the machinery and protocols, and generally get things to the point that the system is no longer the point of failure when running experiments on humans. Instead it is common to see series of publications on new imaging methods and contrast agents which grind away at small animals with no visible attempts to progress upward, which pushes back the time at which you can actually learn how the system works. Publishing this way is far safer but ultimately pointless: drugs for Alzheimer's is a classic case of optimizing for animals and completely missing in humans.

This is at least partly why pre-registration of experiments is becoming normalized, as it is in human clinical trials. The goal here is to require basic statements of purpose and methods prior to execution, such that it is possible to improve the (often quite expensive and time-consuming) experiments beforehand and not during the manuscript review process. Many research groups lack this internal quality control and as a result some institutions are stepping in to require or provide it.