There are different modes in which 6500 can operate. The original 15Mpps mode (30Mpps is architecturally the same thing at higher clock speed) involves the line card arbitrating for a shared parallel bus on the backplane, transfering relevant data through this bus to the sup and after getting the result it transmits the whole packet over another shared parallel bus to the egress line card. In this mode the actual data do not traverse the sup card. In the newer dCEF modes there is a switching fabric of point-to-point source synchronous links and the crossbar switch of this fabric is physically located on the supervisor cards, so the “720” in “sup720” really means that there is 720Gbps of switching bandwidth on the card (although it is not exactly tightly coupled to the rest of the card that implements the “supervisor” itself, to large extent it is colocated on the same card due to physical convenience of that design, IIRC it is actually implemented as a mezzanine board).

At ~400Mpps doing the routing decisions in software is going to be a significant bottleneck even with some kind of modern SoC. But OTOH, today you can design the whole thing in bunch of other ways, as it is significantly easier to implement something with large amount of separate RAM blocks connected through some random arrangement of buses and crossbars controlled by few tightly coupled CPU cores as a one big ASIC (or even FPGA).

But all that assumes that the thing you are building is functionally an L2 switch, maybe designed with ridiculous amount of L3 acceleration (which is exactly what 6500/7600 is). As a point of reference C7200 is a router roughly contemporary to 6500/7600 and architecturally it is just a MIPS-based SBC with six PCI slots.

256 next hops isn't enough. Typical ASICs support 20,000 to 160,000 next hops FECs.

Cisco tried caching routing decisions from non-line rate routing engines in the 90s, and the industry learned the lesson that it's a bad idea. Caching works until you overflow the cache for some reason, and then the box completely falls over as it thrashes.