Based entirely on my experience with Tor, I imagine that this would slow things down considerably.

Mmm, there's nuance with a bit of ambiguity here and I'm not deeply familiar with onion routing (security isn't my specialty, I know enough to say that I'm very out of my depth).

Let's back up to what a VPN does: it's effectively a detour for your network traffic. Instead of traffic going from your client (I'm grouping computer/ phone and routers tougher, because you can do VPN routing at either level) and to whatever you were trying to go, the VPN server acts as a middleman. (Assuming secure traffic ssl/ https) A VPN masks your traffic from your ISP (because they just see you connecting to the VPN instead of your destination) and from your destination (because they see the request as coming from the VPN server*).

As I understand it, onion routing conceptually similar to chaining multiple VPN hops together, such that each hop is only aware of where to go next. (I think technically, each packet is sent along a different random path).

So. There're a couple of ways to answer your question, depending on how you interpret it or how you layer technologies.

1. Onion routing on its own would theoretically already have the privacy advantages of a VPN- because of the way requests are bounced and split up, the receiving end doesn't know where the call came from. That assumes that whatever the client is trying to talk to accepts onion traffic and can talk back over the same protocol.
2. Otherwise, you have to have a client on the other end of the onion route to accept your traffic, make a call to whenever you were trying to go and send it back to you. At that point you've more or less made a VPN.
3. You could go through a VPN first and then onion route, effectively this would decouple your machine from the onion network, but it does put you back at 1 or 2 for actually getting the data you want.

All that said, the major downside to onion routing is speed, it's incredibly slow to break your request apart, bounce it around the network a bunch of times, reassemble it on the other end, and then turn around and do it again for the return trip.

* That also means that some sites, like reddit (fuck u/spez), will block traffic from VPN servers because multiple people's traffic all coming from the same place looks a lot like spam.

You can absolutely self-host onion services and bypass the use of VPN, if you're serving web apps.

Entirely depends on your use case, though.