I can tell you that for DVB-C it's theoretically possible to use a cable modem as tuner. I have a 32 channel DVB-C tuner based on a cable modem which can send around 1.5 Gbit/s of TV streams towards Tvheadend. However, it's all selfmade and there is no such "big" server available commercially as far as I'm aware.
You're basically looking for SAT>IP, there are several servers available. However, I'd rather use some PCI card as those SAT>IP Servers are rather expensive.