According to this Stack Exchange post from last year a full IPv4 routing table requires on the order of a few hundred MBs of RAM. This is indeed a tiny fraction of the cost of maintaining the global internet infrastructure.
The problem is that the routers that have to hold the routing table can only handle a limited number of routes. There is a good article from APNIC about the topic.
And besides, there is no need to keep the whole routing table in RAM. Instead all that's necessary is a single integer per route representing which port packets to each route needs to be sent down. So even for a large router with 64 ports, the whole routing table fits inside 1 megabyte.
bauruine|3 years ago
https://blog.apnic.net/2021/03/03/what-will-happen-when-the-...
pifm_guy|3 years ago
And besides, there is no need to keep the whole routing table in RAM. Instead all that's necessary is a single integer per route representing which port packets to each route needs to be sent down. So even for a large router with 64 ports, the whole routing table fits inside 1 megabyte.