Many of my favourite sites have useless 'light' mobile versions and even if there's a link or switch to toggle the mobile version to 'off' it seems to revert the next time rather than using cookies or whatever to remember my preference.
Personally I want my Internet experience when mobile to be as close as possible to that I get on my desktop. It may not be a universal view but I cannot believe I'm alone in being irritated by site designers assuming I want a lousy half-cut version of their pages.
Yes, I can see the reason to "mobilise" websites very slightly - perhaps some tweaks because it is expecting touch rather than mouse, or browsers on devices with no "end of page" key. But complete redesigns are an anachronism, based on an expectation of 2G networks, limited browsers and small screens, in a time when we're moving to large screens, enough processor speed and zoom/pinch/drag tools to zoom around a full page.
I strongly suspect that much of this nonsense is down to "digital media agencies" and their ilk, insisting that their clients double their web spending to create mobile-specific sites. If I was running a larger site, I'd certainly make sure I got three or four separate opinions before running down this particular blind alley.