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It's not uncommon for some devices have interfaces that the device cannot maintain full wire speed; many software based routers come to mind.
So why have such interfaces? Well, perhaps the device can maintain throughput higher than the next step down in Ethernet. For example, in your case of an ASA that can maintain 5 Gbps, if you only had a gig interface, you could not take advantage of the additional capacity.
Could you use a 3650 instead of an ASA, for basic BGP routing? Sure, but the 3650 doesn't offer the firewall features the ASA provides. The question is, do you need those features?
Am I correct thinking only switch processes information in hardware and ASA + router process it in software
Perhaps, perhaps not. Switches generally do try to process most of their traffic in hardware, but they do some processing in "software", generally control plane "stuff". Something like an ASA might do much of its processing in "software", but newer "software" processing devices sometimes have additional hardware to accelerate some features, off-loading their main CPU (and/or they have multiple CPUs).
