Agreed, the music is lossy to begin with. Most conversions convert the original source back to an uncompressed file before it re-converts it to your new format. (Note: by uncompressed file I mean that it is mathematically uncompressed but the resulting file still is missing whatever data was lost in the original compression.
Then, when you re-compress it, it will very likely change it once again as different compression algorithms, and of course different bitrates, will apply the math differently.
I'm unfamiliar with how streaming format is converted to storable formats like .mp3 or flac but it probably does the same thing. If it directly converted you would be applying some kind of compression algorithm to an already compressed file/stream, which I'm guessing, results in even more variation from the original.
How much of all this will hit your ears in the end? I guess that depends on a lot of variables. Also, I'm no expert, this is all just surmising from my limited experience and reading.
I'm Riffing. People usually stop me when I'm riffing. Or carry on without me. That's also an option.