Your assumption that Apple can design and have TSMC/Samsung manufacture a $30 chip that is competitive with core i3-i7 performance levels is off base. There is a reason why Intel charges the prices it does, yes some of that is to maintain its margins and doesn't have much competition in the x86 space (AMD has not innovated enough to drive Intel's chip prices lower. But most of that is to cover the vast expenses that are realized in the operation of their firm, that is R&D. It should be noted that Intel's ULV processors are in the $200 range.
I believe that Apple does have the potential to be performance/power competitive with Intel (core) based on the amount of resources (cash) that they have, but on the same node (which they won't have access to). However, potential doesn't equal results, and implementing that is much harder than you're assuming.
Also keep in mind that Intel is also innovating, in order for Apple to design a competitive solution when compared to Intel's core line they have to catch up, and they'd be catching up to a moving target. They will have ups and downs, but that is not to say they can't do it, its just unlikely that they would. Its all about cost/benefit, if they want to wean themselves off Intel for their Macs, they will and it will take time, but they'd be giving up top of the line performance, process node, and a valued supplier.
The quad-core Intel core i7 haswell processors are around 180mm^2 in area and have 1.5bn transistors. The A7 in iphone 5s is 100mm^2 and has 1bn transistors. The A7 already has higher transistor density but I guess that is because of the larger area given over to the GPU. The Intel core i7 transistor costs $450-500. The A7 costs $19 (as reported by IHS). These are on different process nodes - the Intel processor is on 22nm Finfet and the A7 is on 28nm planar.
So, on a 20nm scalar or 14/16nm finfet (which will have nearly the same transistor density) an Apple chip will have 2bn transistors in 140mm^2.
You think Samsung/TSMC will charge $200 for it instead of the $20 they were charging for 100 mm^2 in 28nm. I think Apple paying $30 for a chip of die size of 140-150 mm^2 is reasonable. The difference between $30 and $500 that Intel charges (or even $200 core i5 processors) are the monopoly profits accruing to Intel.
On the process node difference - both Intel and TSMC/Samsung will be on 14/16nm finfet in 2015. Yes, Intel will still be a year ahead in introducing 10nm (but then who knows, it might depend on whether/when EUV becomes available).
On moving targets - The ARM camp has been doubling its processing power every year in the last 5 years (that includes both architectural and process node improvements). In the last few years, Intel has done around 10-15% CAGR. So yea, both are moving targets but one is moving significantly faster than the other.
On R&D etc, the point is that it takes much less resources in terms of manpower and time to design on the new ARM architecture as AMD mentioned the other day. One of the reasons for that might be the burden of legacy that x86 code is carrying.
So, Apple hires a ton of talented chip designers (which it started doing a few years ago, and also bought PA Semi and Intrinsity) and gets them to work on the new ARMv8 64bit. Given the same number of transistors, they will take some time to get to where Intel is, but they are also starting from a cleaner slate and have the learnings of x86 to fall back on.
So, if you are standing in mid-2015, with both Intel and TSMC/Samsung/GloFo on 14/16nm Finfet, it should be theoritically, and I am betting practically, possible for chip designers from Apple to design a chip equal to or better than the best Intel processors with a lower power consumption and 1/5 to 1/10th the cost of the core i7s. But we will see what happens...