You can get a glimpse of it, when you don't do the
./nodebb setup and instead just go right into
dev. NodeBB will start into the web installer on port 4567. Of course you would still have to issue that one command, though.
edit: And I presume, that those hosters won't give you access to port 4567 ^_^
The problem in general being: Software written in e.g. php is not a complete program itself. It's merely leveraging an already set up web server. You can upload your files and call the URL, the rest is handled by the server software (Apache or what have you).
But as Scuzz mentioned, a web-installer seems to be in the making. That again lets me guess, that the guys are working towards easy integration the likes of where a hoster can offer their customers a "Click here to install NodeBB" button, which invokes a bunch of scripts setting up your (virtual) server, starting the NodeBB (which actually is not only the forum, but the whole web server* also) and finally redirecting to the web installer. In comparison many uncertain steps, which will have to be clarified between NodeBB and each and every hoster. That's why this will still take some time, I'd say.
*weeell... that's not very acurate either; but this is pretty tl;dr as it is