But it isn't feasible. On the server side, you can stuff a number of virtual websites behind a single IP, but many customers want their own VM (sometimes for very good reasons).
Reverse load balancers could be an option here if/when IPv4 prices rise to a level where the IPv4 address is a significant part of the cost of a VM.
There are things other than http(s) on the net.
While obviously literally true afaict services other than http(s) and mail are the exception not the rule.
On the client side, there is a matter of administrative control. Who will own the NAT device that you and your neighbors all sit behind so that you can be NATed behind a single IP? Do you want to leave it up to your ISP if a rule can be added to the NAT box so you can ssh into your network through a selected port?
Just because you and I don't like the implications of something doesn't make it unfeasible.
It sounds more like a desperate last resort than a real solution.
Compared to that kind of pain, upgrading to IPv6 is a no-brainer.
For better or worse the internet lacks any strong central authority. If it had one maybe we would have had ubiquotous deployment of IPv6 in the 2000s allowing for an IPv4 sunset now.
That hasn't happened though, there are still loads of clients and servers that are IPv4 only (including the one we are discussing this on).
So the choice now is not between "deploy horrible mechanisms to keep IPv4 on life support" and "deploy ipv6". The choice now is between "deploy horrible mechanisms to keep IPv4 on life support without deploying IPv6" and "horrible mechanisms to keep IPv4 on life support and also IPv6".
While i'm in favour of the latter denying that the former is an option is just self-delusion.