I’ve never seen anyone use any formatting within Ruby text, and both Japanese and Chinese traditionally lack both bold and italic, so it most definitely isn’t too important.
I don’t think there’s a reason to explicitly forbid it, though. Since formatting is available in regular CJK text (あいう), it might as well be valid within the base text of a Ruby tag. I can also imagine a scenario where someone would want to emphasize a certain part of pronunciation ("She actually says ［寂］【さ**み**】しい in this case"), in which case formatting in the actual Ruby text would be useful. None of those would be particularly common, I don’t think, but it could become a minor thing people would stumble over every now and then.
The one thing that might get weird is ending a formatting block within a Ruby block. For example, *Italic outside［italic base］【italic ruby* normal ruby】. Either formatting could be disallowed within Ruby tags, or this could result in something like:
<i>Italic outside</i>
<ruby>
<rb>
<i>italic base<i>
</rb>
<rt>
<i>italic ruby</i> normal ruby
</rt>
</ruby>
I suppose it could also introduce a new “context” where new formatting tags can be started but earlier ones can’t be completed… I’m sure you’re more experienced with that kind of thing than I am, though – it’s bound to have come up with other elements before. Stick to what CommonMark usually does, I guess.