The reason why routers are so underpowered is that nobody uses multicast. If there was a strong demand for multicast I'm sure that the manufacturers would increase the capacity of their hardware.
If you build it and it costs less than 6 figures USD, you will drown in customers. It would not be used primarily for multicast at first, it would be used to get BGP working better, but every major ISP would want your router.
Using P2P does not lower the total load on the network, it just spreads it out more evenly.
Correctly done P2P sends traffic through the best route, typically from someone on the same ISP as the recipient and preferably from the same neighbourhood. That lowers total load a lot. Most current P2P networks do not particularly worry about optimal routing; they are much more constrained by traffic shaping or (often artificially) limited last-mile upstream capacity. It would be fairly easy to give priority to low-latency peers.
Besides, P2P can solve the problem of subscribers not watching at exactly the same time. Multicast breaks as soon as someone presses pause.