There's a whole lot of personal frustration on watching a group of testers take requirements, take designs of how the software is to be built, design test cases, automate some of them, execute others manually, take 10x more time than I think they should AND leak relevant problems to next stages in a way that makes you question if they were ever there in the process.
Your test cases don't give me comfort when your results say that the work that really matters - information on quality of the product - is lacking. Your results include the neatly written steps that describe exactly what you did so that someone else with basic information about the product can take them up next time for purposes of regression. Yet that does not comfort me. And since existence of those tests makes next rounds of testing even less effective for results, you are only passing forward things that make us worse, not better.
Over the years, I have joined organizations like this. I've cried for the lack of understanding in the organization on what good testing looks like, and wondered if I will be able to rescue the lovely colleagues doing bad work just because they think that is what is asked of them.
Exploratory testing is not the technique that you apply on top of this to fix it by doing "sessions". It is the mindset you intertwine in to turn the mechanistic requirements to designs to test cases to executions manual and automated into a process of thinking, learning and RESULTS.
Sometimes the organization I land in is overstructured and underperforming. If the company is successful, usually it is only testing that is over structured and underperforming, and we just don't notice bad testing when great development exists.
Sometimes the organization I land in has really bad quality and testing is "important" as patching it. Exploratory testing may be a cheaper way of patching.
Sometimes the organization I land in has excellent quality and exploratory testing is what it should be - finding things that require thinking, connections and insight.
It still comes down to costs and results, not labels and right use of words. And it always starts with requirements.