Every device I know of defaults to sRGB. No color profile is needed if you have worked in the sRGB space. Another reason to stick with it for media intended to be shared digitally.
I have two so-called sRGB monitors on my desk at work - I can't get them to look anywhere close to consistent. I need to go in some weekend with my ColorMunki...
All my output images at the moment are sRGB, and I make sure that profile is embedded. I think it was okay to just assume sRGB until recently, higher gamut displays are becoming more prevalent. Even with a sRGB image, having the embedded profile available helps those using color-managed software on higher-gamut monitors to handle the image as best as possible, with the appropriate rendering intent.
Edit: Just thought about the last sentence a little more, rendering intents AFAIK are about handling out-of-gamut colors. I'd be interested in hearing from anyone with experience displaying sRGB images on a high-gamut monitor with color-managed software - how did it look?
There were some issues (primarily over saturated reds) with web page colors and untagged sRGB images. The issue was mostly that, other than Firefox*, browsers were not color managed, in the sense of rendering into the monitor color space.
Chrome now seems to render into monitor color space as well (both seem to be using perceptual intent)
*and in FF, you have to enable it in the settings.
Have a look at
this page for a discussion (and a test untagged image with overlaid tagged image that shows whether your browser is managing colors properly or not.
I'd not worry about how tagged sRGB looks on WG monitors. Folks who've spent the extra $$ for them have probably also gone to the trouble of turning on color management in Firefox - and it seems to be on by default in the recent versions of Chrome.