In a manner of speaking, when you perform array (“indexed”) type addressing with general registers, you are doing essentially the same thing as the segment registers. In the bad old days of 8-bit and 16-bit programming, many applications required much more data (and occasionally more code) than a 16-bit address could reach.
So many CPUs solved this by having a larger addressable memory space than the 16-bit addresses could reach, and made those regions of memory accessible by means of “segment registers” or similar. A program would set the address in a “segment register” to an address above the (65536 byte) 16-bit address space. Then when certain instructions were executed, they would add the instruction specified address to the appropriate (or specified) “segment register” to read data (or code) beyond the range of 16-bit addresses or 16-bit offsets.
However, the situation today is opposite!
How so? Today, a 64-bit CPU can address more than (not less than) all addressable memory space. Most 64-bit CPUs today can address something like 40-bits to 48-bits of physical memory. True, there is nothing to stop them from addressing a full 64-bit memory space, but they know nobody (but the NSA) can afford that much RAM, and besides, hanging that much RAM on the CPU bus would load it down with capacitance, and slow down ALL memory accesses outside the CPU chip.
Therefore, the current generation of mainstream CPUs can address 40-bits to 48-bits of memory space, which is more than 99.999% of the market would ever imagine reaching. Note that 32-bits is 4-gigabytes (which some people do exceed today by a factor of 2, 4, 8, 16), but even 40-bits can address 256 * 4GB == 1024GB == 1TB. While 64GB of RAM is reasonable today, and perhaps even 256GB in extreme cases, 1024GB just isn’t necessary except for perhaps 0.001% of applications, and is unaffordable to boot.
And if you are in that 0.001% category, just buy one of the CPUs that address 48-bits of physical memory, and you’re talking 256TB… which is currently impractical because it would load down the memory bus with vastly too much capacitance (maybe even to the point the memory bus would stop completely stop working).
The point is this. When your normal addressing modes with normal 64-bit registers can already address vastly more memory than your computer can contain, the conventional reason to add segment registers vanishes.
This doesn’t mean people could not find useful purposes for segment registers in 64-bit CPUs. They could. Several possibilities are evident. However, with 64-bit general registers and 64-bit address space, there is nothing that general registers could not do that segment registers can. And general purpose registers have a great many purposes, which segment registers do not. Therefore, if anyone was planning to add more registers to a modern 64-bit CPU, they would add general purpose registers (which can do “anything”) rather than add very limited purpose “segment registers”.
And indeed they have. As you may have noticed, AMD and Intel keep adding more [sorta] general-purpose registers to the SIMD register-file, and AMD doubled the number of [truly] general purpose registers when they designed their 64-bit x86_64 CPUs (which Intel copied).