I run a fully remote company, and most of the objections I've heard from others we've found workaround for.
The biggest unsolved problem is whiteboarding - there is no good collaborative online whiteboarding solution that doesn't require a lot of expensive equipment to be deployed to everyone.
If you really must, give everybody a Wacom tablet + Paint + Screen sharing (or just a VNC server over the VPN so everybody can draw)
Maybe my company is just weird, but we don't use whiteboards all that much. At least for code our preferred collaboration method is pairing, which isn't as hard over a network.
We write NLP software, and most of our whiteboard usage is for drawing out linguistic constructs and often involves only one person doing the drawing, which seems like an easy subset of whiteboarding to handle remotely.
Edit: I found another called deekit.com
Looks like there are a few other options: