Are there any generic KVM over IP cards/chips for motherboards without any such capability?

You'll need to check with your specific motherboard vendor to see what's available. There won't be anything generic that works with everything unless it was going to be able to physically push the power button on the server.

There used to be a company that made a card (ISA or PCI models) that did this: it was called PC Weasel. They appear to be defunct, although you might be able to find some on eBay.

Other than that, it looks like any given IPMI/BMC card has to be supported by the mobo it's getting attached to, reading up on the SuperMicro and ATEN product docs on their IPMI cards.

As I mentioned in comments, you can get a per-port controllable PDU and an IP KVM for all of your servers, and you've got a good chunk of the feature set. The nice thing about Tier-1 servers and their cards is that they also implement remote mounting of media for OS installs, monitoring hooks for the hardware, buncha fun stuff.