The answer is: it depends!
We don't know the industry or the type of software you are testing and not all software is created or used equally.
whereas maintaining test cases is not important
What's important to you may be different for someone else. While you may not find it important or necessary, others will! And, there are reasons to do so other than to satisfy PMs!
A lot of people like to separate Quality Engineers and Testers into different categories. (Personally, this is unfair as it simplifies the skills and experiences of so many in the Quality and Testing field!) So, depending on which category/job title you have, writing test cases may not be a good fit. It may also not be a good fit based on your own skillset, experiences, knowledge of the role, etc.
Let's break down some different perspectives.
Someone is new to testing: they likely have a high need to write down test cases in order to gain confidence in themselves and confidence from the team to ensure the software is well-tested. A lot of non-testers don't understand the role, so writing down test cases can help them understand the work you are doing and you can help educate them on your role. Others see it as a form of being transparent. If you expect devs and PMs to share requirements and code with you, shouldn't you also be just as transparent about your process, and your test cases with them? If they are not new but learned via this approach, they may find continued value just out of habit.
Someone that processes information differently: People think and organize their thoughts differently. Some do so via speaking and audio, some do so via writing (outlines, detailed plans, etc), and others do all of them. There's no right or wrong way to think or organize your thoughts!
exploratory testing notes which include different test ideas, scenarios, heuristics-based test design ideas, any other ideas, etc
These are all good techniques we all should be aware of and know when to use them and you may be able to only do just that, but not everyone can.
Someone doing test automation: If you prefer or your role calls for a majority of your time automating test cases, one, you may have a need for someone else to write those test cases for you so that you can automate them. Second, if there is no one else but you, you may just prefer to write those test cases in code. Personally, once a test is automated, it really doesn't need to be in a test case management system as the test automation serves that purpose.
Regression testing: regardless of test automation status on the team, having written tests helps speed up the testing process as you don't have to recreate work you've already done! This allows you to organize and categorize test cases by feature, priority, severity/importance.
Audits: Some industries need an audit trail of all work performed. Industries like automotive, aeronautical, medical, and anything involving safety around life/death. Government regulations are also another reason why an audit trail is important here. By having written test cases in a management system, it helps with those audits.
There are certainly more reasons and perspectives than just these! And often, these perspectives overlap; it's not a one size fits all situation.
Remember, software is complex, and how people simplify and organize that complexity will differ.
Personally, I don't like using test case management systems. I prefer the old school "let's just use Excel" way of writing them!