That's because you can't make a Ghostbusters sequel that isn't too faithful to the original because it's Ghostbusters and there's only a few things about it that make it Ghostbusters that you HAVE to have in it.
IE making a new Ghostbusters movie in the first place was a dumb idea. Original cast or not.
Paradoxically, I think making a reboot gives Feig LESS freedom than making a loosely tied sequel. Making a reboot, there are a number of things you have to have or it's not really Ghostbusters, and it ends up being really similar to the original.
It's actually probably easier to go Lost World and acknowledge all of this stuff happened at some point, but it was a long time ago and no ghostly activity since and the ghostbusters retired, moved, died fighting ghosts, lost in an inter dimensional rift, whatever.
And the new crew has to basically pick up from scratch. It would have given them more freedom to say "hey these aren't the original crew, so they are doing everything a bit differently... But all of that original stuff is still valid!"
Also, it gives you room to have a bunch of spin off media showing what happened to the original busters.