That probably sounds like a strange question. 6 > 4, and IPv6 is simply the newer version of IPv4. Everyone will eventually be upgraded, right?
That's not really accurate. IPv6 is not backwards compatible with IPv4. Despite the name, it's really a different protocol. From a technical perspective, asking if we will all upgrade to IPv6 is similar to asking if we will all sidegrade to IPX. The only difference is in the branding. IPv6 sounds like an upgrade.
Dan Bernstein has a great article up on the technical issues with migrating to IPv6. In general, the plans that IPv6 advocates are discussing involve every node on the Internet upgrading to support IPv6 and IPv4 simultaneously, and then we can make a big switchover. At first blush, this sounds like a good plan. It worked for HTTP, and as Bernstein points out, it worked for MX records for SMTP servers. However, so far at least, IPv6 isn't designed to work that way.
The problem is that, unlike with these other examples, it's not a simple software upgrade to simultaneously support IPv6 and IPv4. Most distressingly, every node on the Internet needs to additionally have an IPv6 address. That alone is a fatal flaw. It's simply not going to happen. With the MX record transition, nodes without an MX record simply fell back on their A record, which they already had. With the HTTP transition, HTTP/1.1 was and remains an optional extension. Every node can always fall back to HTTP/1.0 or even HTTP/0.9. With IPv6, however, any node that doesn't have an IPv6 address simply doesn't get to play.
The same thing is happening with DNS. In addition to allocating all those IPv6 addresses, you need to add them to DNS. Until every DNS record is updated to have both IPv6 and IPv4 addresses in it, it's not possible to flip the switch.
As a separate issue, does anyone really care about the other features of IPv6 other than the extended address space? IPv6 comes with a host of features, and some of the more complicated and computationally expensive ones like IPsec are mandatory. These strike me as things that would better as optional extensions, and indeed, most of these features except the larger address space are already being explored as such.
Overall, the main thing that IPv6 brings us over IPv4 is the larger address space. Why not make that an optional extension, too? The IP packet format already allows for extensions. Routers trying to forward an extended-address packet could simply ping each other before doing it, and if the next router in the chain doesn't support them, bounce back a "host not reachable" packet. Lots of software would need updating, e.g. the socket APIs used on end point software would need to support optional, longer addresses. However, the changes would be much smaller than are required to support IPv6.
So if the best transition to big address spaces is to extend IPv4 rather than stage a simultaneous leap to IPv6, what is going to happen? One possibility is that such an IPv4++ will be designed, it will be rebranded as IPv6, and everyone will simply ignore the failed experiments with a more radically different IPv6. Another possibility is that such an IPv4++ will be rebranded as IPv7. This is all branding and politics, though I must say that the most honest thing would be to simply call it IPv4.
Another possibility is that everyone interested in big addresses will get suckered into the IPv6 quagmire, and it just won't happen. This isn't clearly a bad thing. The "small" address space of IPv4 is plenty large if we continue to have an Internet that is a patchwork of interconnected networks rather than a true globally controlled network. With the smaller address space, my coffee maker can still send a packet to your coffee maker, but from each coffee maker's perspective it will be sending packets out into the cloud. That seems healthy, to me. Perhaps you want to support virtual coffee makers, or to have transparent coffee maker failover. It's not really my business exactly how you route my packet in your network. Why would you want to export a node address to me that tries to pinpoint a specific machine?
A more exotic possibility is that some other network gains market share. Some network that offers real, pressing advantages, unlike IPv6. A packet-switching network protocol is like a social network or an instant messaging system. New networks take over old ones by initially offering something attractive enough that people will operate on both networks simultaneously. Once enough people are on the new network, they can start taking it for granted, and the old network can deflate in usage very rapidly. Really, though, what possible improvement would the packet switching layer have that would encourage that initial batch of people to use the new one in parallel to the old one? Clearly it's nothing in the laundry list of features in IPv6, because adoption has been really tepid. Further, all the really good network improvements have been possible to retrograde onto IPv4.
My best guess is that we continue on with IPv4 plus extensions. More tentatively, I would guess that we never get around to extending it for larger address spaces. If larger address spaces do become a pressing concern, however, I'd expect IPv4 to be extended rather than for the whole world to waste time on switching to completely new protocol. It's just good engineering.