The problem isn't that IPv6 isn't backwards compattible. The problem is that IPv4 is not forwards compattible.

Arstechnica has an article about it: http://arstechnica.com/business/2016/01/ipv6-celebrates-its-...

I wonder if it couldn't still be accomplished at this late hour. An RFC to reserve 32 bits of an IPv6 Address along with a logical (read: Easy to remember) remaining 96 bits might be in order.

In theory - and if I remember correctly - you can embed IPv4 addresses into IPv6 addresses.

The prefix should be all zeroes, so you get something like: ::12.123.99.222 Which is not that hard to remember. :P

Could they modify IPv4 in a backwards-compatible way, allocating more address space to that part of the TCP header for example? And including perhaps a version flag?

In fact I'm not sure why it wasn't done that way to begin with, unless IPv6 fixes a bunch of other problems I was not aware of

Yeah, they really didn't think though the transition when designing IPv4.