You will never always return the same results
This is important to remember. For various reasons, the SRP for any given terms is usually a slowly changing experience. The merchandise and inventory change, so the results should change. Maybe not today or tomorrow. But at some point, things are dropped and things are added.
So, if it's not an immutable list of constants, what level of change will your users tolerate. Chances are, more than you think.
The age of data science and machine learning
I tested an algorithmic SRP ranker nearly 10 years ago. It was pretty early for data science applications in mid-level e-comm applications, but the human intervention model was too "emotional". If we had a big day with lots of data (a few hundred thousand hits), the model might return something new the next day. It worked. Conversion rates saw a double digit lift.
10 years on, ML is everywhere. Digital products respond to people's needs. If the model is good (and remember, humans do write these models), then it will get things right more than it gets things wrong.
Users now expect their digital world to respond to their behavior and needs.
On the topic of search ranking methods, this data science article makes a keen observation:
When you reach a scale where incremental gains in relevance are more important than the rest of the factors, consider moving to an ML model. But do make sure you have a good answer to the “Optimization Metric” problem before you start working on a ML model.
The operative phrase there is "incremental gains". You need a lot of data coupled with a well-tuned model to slowly improve the performance (engagement, conversion, average order, etc). IOW, the results are not erratic.
Too big for human orchestration
And just to further emphasize a critical point with AI / ML: you are operating on massive data sets. As pointed out in this Forbes article, man + machine can do more.
… machine learning provides significant value by processing vast quantities of data to find patterns, drawing conclusions no human is capable of and enabling incredibly precise, data-driven activations for marketers.
If you have a large catalog, you probably have a lot of users, and even more data. ML-driven SRPs are likely to prove fruitful.