I think the site is using a slightly sensationalist headline, as the halo - which I wouldn't consider a closed cockpit any more than a role hoop - is currently much more likely than a proper closed cockpit.
Personally though I'm okay with a fully closed cockpit. Formula 1 to me doesn't necessarily have to mean "open wheel racing", to me it's more about "the most advanced/prestigious racing". It's about state of the art technology being raced in exotic/historic locations with top brands. Open top racing is cooler, yes, but if a cockpit makes things that much safer I'd rather have it.
Besides, I'd much rather watch this racing around Monaco:
Than this:
To me the lower nose requirement (hello submarining) was much more knee-jerk and ill-thought-out.