Yes, Richard. Even a $1 ARM does have auto-increment/auto-decrement. Cheap or expensive just affects amount of RAM, flash, max clock speed, pins and peripherial bells and whistles. There will still be an ARM core inside, or it wouldn't be an ARM chip.

With the possible exception of some 8-bit processors, there are hardly any new processors released for a good many years that does not have auto-decrement and auto-increment as standard - normally not on one or two dedicated index registers but as standard on the full set of general-purpose registers. The 32-bit processors have the advantage that they normally don't need dedicated index registers since a general-purpose register is wide enough to address 4GB of memory space. Removing the separation between GP registers and index registers means that you get the full advantage of multiply etc (Ax+B is a required operation for finding the offset of an element in an array) but when performing indexed lookup, many of the processors also have a separate addressing engine to allow the sum of two registers (or a register + offset) to be used - and to allow one of the values to be scaled, representing the stride size of an array.

Auto-increment/decrement are not seen as features, so they are not mentioned in any feature lists. The availability of them are similar to the availability of an ALU.

Last time we discussed this, I did mention this. But the chip I used for comparison at that time ended up (I think) at 72ns while your 8051 managed 60ns. So you decided to ignore ARM processors. But there are many, many ARM processors available and they span a large performance range just as 8051 chips does. And there are many other architectures that also may be applicable for a design. The biggest advantage with ARM chips isn't that they are the worlds best processor cores, but that the same set of tools can be used with so varying chips. ARM sells the core, which means that the manufacturers will have to spend time making their chips unique and well-placed by making sure that they add the peripherials that the end-users wants. Almost all of the competition is the availability of good add-ons at a low price. The same thing doesn't normally happen if looking at 32-bit processors of other architectures. Atmel and PIC have proprietary 32-bit architectures, reducing the competition. And there are too few PPC or MIPS manufacturers.

A normal 100-pin chip with 0.8mm spacing is harder to hand-solder for a single prototype. But not more expensive for real production. It does not require extra high-grade PCB and it is well within the capabilities of the standard component pickers/placers. Nothing strange with soldering them either. The ability to get a 48-pin or 100-pin or 144-pin or ... chip means that each and every design can optimize the amount of external components.

The $1 price I mentioned is not for single unit - when I need a single unit of something, I don't care about the price unless it is consuming a significant percentage of my salary.

I mostly use NXP ARM chips, and I think the $1.5 .. $2 price I mentioned was $2 at 100 units (a chip in the LPC13xx series). The NXP chips are not the cheapest, but they tend to have very good peripherials making the chips nice and easy to use.