The difference is that very, very few organizations require blocks that enormous in IPv6. And the ones that do will most likely never need to ask for more. (For comparison, Comcast, the largest home ISP in the US, has a /20.) But in IPv4, a /16 (or smaller blocks adding up to one) is nothing for even a mid-sized ISP.
Also, the allocation policies are much different. In IPv4, allocations are made to being as small as possible (while still meeting immediate needs) in order to conserve addresses. The cost is that the routing table grows like crazy, since network operators need to keep coming back year after year (or sooner) to get more address blocks.
In IPv6, allocations are made to cover the network operator's long-term needs so that they won't have to get a second, non-contiguous block. By "wasting" address space you cut down on routing table size, since even very large networks only need to announce a small number of routes.
Even with this "waste", we've only allocated a tiny amount of IPv6 space. None of the RIRs have had to go back to IANA for new IPv6 space since 2006[1], even with allocations ramping up in the last few years. (And IANA only gives the RIRs a /12 at a time.) We seem to be fine for the foreseeable future.
But even if somehow we do start using up too much v6 address space, the good news is we can always change allocation practices. Let's say in 2040 we realize we've used up way more of the IPv6 space than we expected we would by then. The RIRs can always change their policies, favoring conservation over smaller routing tables like they used to with IPv4. I seriously doubt that will happen within any timeframe we can reasonably make predictions about, but if it does, we'd have a lot more flexibility than we did with IPv4 depletion.
[1] https://www.iana.org/assignments/ipv6-unicast-address-assign...