But, is this necessarily a requirement of routers? Does DHCP/NAT imply (or necessitate) concealment of mac addresses? (i.e., of devices wirelessly connected to the router)
First of all, neither DHCP nor NAT are a requirement of routers... and on the opposite side, providing a wireless connection does not require a router.
But besides that – yes, "routers" are devices which handle IP packets without the MAC wrapping. Once the packet is delivered to the router, it throws away the original MAC address and makes the routing decision entirely based on what's in the IP packet, and re-sends the packet with a new MAC header apropriate for the output interface.
This means a router can connect networks which have different kinds of MAC addresses (i.e. not just Ethernet's usual 48-bit). It can even connect networks which don't have MAC addresses, such as ADSL circuits or 3G/4G mobile connections, so long as they speak IP.
It seems it would make the router's job even easier since the packets/frames coming from the internet to its (router) IP address would already have the exact mac address of the device of interest specified right away!
Not really; this would just mean the sender – the second router that's a hop away – would need to know the MAC addresses of your devices instead. That means your router would have to pass through the ARP queries, i.e. it'd still do pretty much the same amount of work it's already doing.
So it would merely shift the work elsewhere, as the second router would be doing basically the same thing as your router does now (ARP queries to learn the MAC addresses), except instead of remembering 1 MAC per customer, now it would need to remember 5 or 10 per customer. The same goes for any L2 switches in between, which do not have infinite memory.
Additionally: MAC addresses aren't always globally unique. They have to be unique on the L2 network, but it's possible for the same MAC address to exist on multiple networks, whether it's due to accidental collisions, or due to special protocols (VRRP "high availability"), or due to some customers being intentionally malicious. Of course, it's possible that even the routers' MAC addresses could collide in some cases, but I suspect that's easier to resolve than end-user devices.
(That's also disregarding issues such as networks which don't use the same kind of MAC header, like 4G.)
But most importantly, this is a router. Its actual job is to decide which device receives which packets based on the IP addresses, according to its routing table (and its conntrack state table if NAT is enabled). So technically you could have a device which works entirely at MAC level, including even NAT, but it literally wouldn't be a "router" anymore.
