I guess so. It is just that so few people would know that this "move" was actually occurring, that it wouldn't be much of a move at all. More like a silent transition.
I like a plan where a.b.c.d address format is changed to an administratively compatible format where each of the four components is a 16 bit number represented in text format in decimal form.
In binary form the IPv4 address C0 A0 20 01 would become 00C0 00A0 0020 0001. All existing address prefixes would be preserved, except in expanded form when represented in binary. In text format the address would be 126.96.36.199 in both cases. Then one day about ten years later, addresses like 300.278.22.1 would become publicly routable. Or even addresses like 6700.45320.658.33781.
A straightforward expansion would allow a variable number of components where the number varied from 4 to 8 or so. That way everyone with an IPv4 style 4 component address could add publicly addressable sub networks without getting a new allocation. The network core would generally only do routing on the first four components (64 bits) for economic reasons, but hardware routers with 128 bit prefix capability would eventually be come common, starting at large edge networks. Trailing zero bits would be implied.
Existing configurations would be preserved, although alternative netmask indicators would eventually have to be added, because a current "/24" would in actuality be a 48 bit prefix, and if you want to specify netmasks that end on any of the inserted bits a different syntax would need to be used. "//48" style perhaps.
One of the other advantages of a variable length addressing scheme like this is that most addresses would only be 64 bits, not 128, significantly reducing the overhead for small packets like those used in VOIP, especially on lower bandwidth connections. Who really wants their MAC address broadcast all over the Internet anyway? For servers, it is practically useless. For individuals it is a privacy nightmare.