The CPU load and the power consumption of a renderer are typically high at boot time and stabilize within a few seconds after boot is completed.
For instance, on the RPi 3B+ that hosts my DigiOne Signature, I measure between 0.5A and 1.0A current at boot and less than 0.4A after boot is completed.
It is conceivable that transients in CPU load and power consumption have an impact on sound quality, but that effect should decay very fast once the system is up an running.
On music servers the situation is a bit different: after boot, they typically rescan music libraries and start administrative tasks that can take minutes to complete.
Perhaps the behavior that you observe has to do with the PSU. In my system I do not need to switch off the PSU when rebooting.
System software shouldn’t anyway have any significant impact on sound quality: If a new version of MPD, a Tidal plugin or a bug fix would impact the sound quality of a device perceivably, we would be at the mercy of chance.
I routinely upgrade my systems and install new versions of upmpdcli, MPD and other application-level software and I never observed any changes in the sound quality.
New device drivers, kernels, etc. can of course have an impact on the sound quality of a renderer. But this is not a software layer that typically needs to be modified to fix a bug or to add support for a new internet streaming service. There are exceptions, of course.
If Naim’s software design does not generally allow to fix bugs without impacting the sound quality, be this for the good or for the bad, then that design is obviously deficient.
I very much doubt this: since the new streaming platform is based on Linux, Naim will most likely use standard Linux components, perhaps with some own specific software, for instance for the UPnP server that also runs on their streamers.
If the software allows fixing bugs without impacting the sound quality, then why do not they clearly distinguish between firmware upgrades that are meant to fix bugs or improve functionalities and upgrades that are meant to improve the sound quality?
They could use even numbers for sound quality upgrades and odd numbers for bug fixes and functionality improvements and one could decide to just upgrade functionalities, sound quality or both.