anyone who compromises [the VPN server] is in a pretty good position.
Sure. But without a VPN, anyone who compromises even one of your other hosts is in the same position. It's a lot easier to audit a single-purpose VPN server for possible security issues than it is to audit all the application code running on the rest of your production systems.
And I'd rate the odds of a 0-day being found at higher for most VPN software than for SSH.
I wouldn't. And even if you're right, getting a VPN login still doesn't get you anywhere. You still have to be able to ssh to the rest of the hosts. That's why we do security in layers.
Routing transparency. Sure, you can script a bunch of tunnels, but it's nice to handle routing at a lower layer. Having worked with both setups, I vastly prefer the VPN solution for ease of setup, use, and maintenance.
Also, different attack surfaces. Two layers of the same security measure (ssh) is, all else equal, not quite as good as two layers involving two different measures (VPN, ssh).
I have experience with many open source VPN servers. The purpose is a bit different -- we provide a VPN service to home users to encrypt their internet traffic. But the same problems should apply.
OpenVPN is the most compatible with a variety of clients. OpenVPN runs in userspace, so the clients for each OS and mobile platform interoperate well. The downside is, it does require a client program to be installed and configured. It's considered very secure, using SSL. Since it's userspace, moving large amounts of traffic means more context switching and higher cpu usage. Despite that, I've found it to be faster and more stable than the alternatives.
L2TP/IPSec is built in to most clients -- Windows, OS X, mobile. But every implementation is different and it's hard to configure a server to work with all of them. There are also more moving parts -- an IPSec server (openswan, strongswan, or racoon), and L2TP server (openl2tpd, xl2tpd) and a PPP server (pppd). IPSec seems to be a secure protocol but it's very complicated. I tend to distrust complicated security.
Pure IPSec has many of the problems of L2TP/IPSec with the added problem of difficult to configure in Windows and OS X.
PPTP is not performant or very secure. Other than the fact that almost every client supports it, I see no reason to use it for a new VPN.