Home embedded routers run into problems due to the overhead of state tracking and buffers for all the simultaneous connections. If they support 10k simultaneous connections, and they track 2x ip addresses for each, the additional overhead of 2x 12 bytes per ipv6 connection is 240kB memory. Buffers are going to be much, much more than that, and buffer requirements are about the same for ipv4 and ipv6.
Routers that have full BGP routing tables tend to be serious routers with TCAM. That's expensive and that does put pressure on BGP routing table sizes, to accommodate older and cheaper [real] routers. However, ignoring ipv6 is simply not an option, so there's no point in dreaming about how staying with ipv4 forever would allow quadruple the routing table capacity for a set amount of TCAM.
As for sticking with IPv4 for increased capacity, it depends. Private networks might get away with it for their internal traffic, but no major ISP nowadays will deliberately choose not to route IPv6 for their customers.