This is a valid concern.
My understanding of your question is that it's a monitoring problem rather than editing problem. That is, when you are editing an sRGB photo, you specify that your current worskpace is sRGB, instead of converting it to AdobeRGB first. In this case, all your editing is happening with full 8 bits (or 16/32 if you select so in the editor) per channel dedicated to sRGB, and you have no losses there.
However, there is still a problem of how to display the result. The chain Editor Output → OS (incl. video driver) → Display. The perfect (formal) accuracy of your editing may be compromised if this chain is 8 bit - and it usually is.
Say, for simplicity, your image has a perfect sRGB green G=255. If your display was a perfect narrow gamut sRGB, the system would eventually send this G=255 to the screen. But an AdobeRGB display can show a greener green, so your G=255 must be converted to something like G=240 for AdobeRGB. I just made the numbers up, but it is evident that you will see fewer gradient steps from 0.
In other words, conversion sRGB → AdobeRGB (or more accurately, sRGB → wide gamut display) is still happening, but past the editor in real time. The OS/driver may be handling the conversion with higher accuracy in floating point, but if there is any one place which requires 8 bit (say, as it often happens, the display itself), you will still have losses and more banding.
To eliminate the problem, the whole output chain must support higher-bit output (in practice, 10 bit). Most modern video cards support 10 bit, but it's never turned on by default. It needs to be turned on manually in the driver settings, but it's not enough. Obviously, the display must support this mode: otherwise you won't see anything. Yet it's still not enough. It's often forgotten that the application also must support it. Photoshop has a special setting to enable 10-bit output. So, this requires quite a bit of compatibility.
The question is: is 8 bit really not enough? will you see it?
My experience is this: no, the degradation is not much noticeable (even on gradients), but only for displays that do colour correction themselves with higher-bit LUTs (often 12-14-16 bit), i.e. professional displays, or if you don't do colour correction at all.
The point is: it is the colour correction that often looks bad with significant banding (esp. on grey gradients), if done in 8 bit. The reason, as I understand, is that the correction curves for each of the three channels are not identical (almost by definition). Differences in quantisation at each point cause colur shifts, and this is much more noticeable than a missing band.
Consumer monitors are calibrated and corrected by the OS or a dedicated software, and the correction is happening in the OS/Driver link of the output chain. Consequently, this usually happens in 8 bits. Professional monitors want the OS to output the plain uncorrected (but still converted to the gamut!) colours, and then correct them to the proper greys with higher quality themselves. This is a big difference. Compared to it, the additional banding due to the grey-neutral sRGB → AdobeRGB 8-bit conversion is negligible.