Only on the first installation, which the installer requests. After that no write permission is needed and I dont see how changing to/from read-only would make any difference
Thank you for taking the time to read this thread.
I've got bad news, I was entirely wrong yesterday. I misunderstood the read-only flag on Windows. Resource usage was back to normal right after 'changing the folder permissions' (must have been a weird coincidence), so I assumed that was the solution. But shortly after making my last post, the CPU usage went back up (same behavior as described in the original post), both with the installed version as well as in the portable version (with or without admin privileges). I was too tired tomake another post in this thread and went to sleep. I'm really sorry for the confusion!
I left Musicbee in idle over the night, but the CPU usage was still the same when I woke up.
After backing up my settings/library to my desktop and scanning my computer for malware, I have manually deleted the Musicbee folders in Appdata\Local and AppData\Roaming, then I uninstalled the software entirely.
I installed the latest version of Musicbee on another drive (i.e. not the system drive), to make sure it wasn't an issue with the hardware. I didn't import my settings or library and played a different file. Same result.
I deleted the AppData folders again just in case and tried the portable version from yet another drive. I left all settings on default, same result.
To rule out any programs interfering with Musicbee, I restarted my computer and disabled as many background processes as possible. I also considered that it might be some bug in the system monitor software I'm using, so I compared the displayed CPU usage with the one in Microsoft's task manager as well as Microsoft's Process explorer. I still got the same results in all three applications.

I also checked for anything out of the ordinary in the Windows Event Viewer, but couldn't find anything.
Musicbee's error log was empty.
I don't know what else I could try to make this go away and I still don't understand why it shortly went back to normal yesterday.
Then I decided to try Musicbee on my laptop (which is running Windows 8.0). It had v2.3.5188 installed. This version on that machine uses around 3% CPU during playback and around 1% afterwards on a mobile i5 3rd gen. So it seems that this is an issue exclusive to my desktop computer. I have not seen anyone experiencing anything similar on the forums or elsewhere on the internet.
I can't think of anything 'special' about this machine that might be causing this and other players don't seem to have any issues with playback/pausing files.
But I love Musicbee and I really want it to work properly on this computer.
Edit:I still had the installer for Musicbee v2.5.5804 on my disk. After installation, the library had all of my files, even the ones I added recently and it uses between 1 and 5% during playback depending on the file and once playback is stopped, the CPU usage goes down to ~0.01%. I'll be using that until another solution for v3 is found.