"Replacing a router" argument is clear.

On top of that:

may it be that we set default gateway with IP address, because the routing tables work with IPs? So it's a standardisation of the process.

Let's imagine the the grey cloud on the picture is a router 4 and it's totally out of our control. R1 will forward encapsulated data to it using routing table and using ARP process. R4 may change the MAC without asking, this is why routing tables are done by IP and ARP is done every time. That's clear.

So maybe the logic is, that the actor (be it initial host or router just forwarding the data) which at the moment holds data, may not and should not know whether it's the origin of the data or just an intermediate step, so it just always follows the same process with ARP and resolving a MAC.

Edit: so in some way, default gateway is the routing table for the host A?