T series parts don't generally include decent integrated graphics which is what Apple have been going after for some years now and it'll be even more important with new Apple branded displays around the corner. Apple currently use 65w parts for the 21.5" iMac (plus a GPU) and then up to 95w parts for the 27" iMac. For economy of scale it would be very interesting to see Apple effectively make a headless 21.5" iMac but they never have.
The new Intel Core G series GPUs are 45w quad core mobile CPUs (4 cores/8 threads) with AMD VEGA built in. They look like Apple driven Intel designs destined for future 15" MacBook Pros. They'd be great for a smaller desktop Mac but again highly unlikely.
I don't believe the profit margin you posit for that Pentium G4560T is accurate in the first place (where is the calculation for macOS?) but it's also not worth Apple's while to develop an almost forgotten line of desktop computers - the user group here might be vocal but it's not large like the laptop people. They'll get big discounts on the same CPUs used in the MacBook Pros.
Cutting back to the chase, I believe Apple will be borrowing from an existing parts bin to make the next Mini if applicable. If they follow the existing pattern you just have to keep looking at the MacBook Pro line for clues but it's up to them if refreshing the mini is worth it or if they just lower the base price of the modular Mac Pro to draw out more people into the $2k money for one.
1) Even the Kaby Lake HD610 graphics in the low-end S/T series processors can do 3 monitors at 4K @ 60Hz. The rest of the entire Kaby lineup is HD630, which really just adds some extra speed (which doesn't matter much)
2) If you want to complain about game support -> MacRumors Chorus: "The Mini has never been a game playing machine"
3) If you want to complain about video/image editing support -> MacRumors Chorus: "The Mini has never been a business graphics workhorse machine"
4) The 'T' series is socket compatible with the 65W/95W 'S' series chips used in the iMacs. The only difference is slower speed and lower TPD
5) Pricing on the VegaM G-series multi-chip modules isn't easy to get, but it's certainly over $500 for the MCM alone. That would likely put the new "base" Mini price in the $1200 range...
6) That calculation is pretty accurate. If you know where to look, you can build out a mini-STX system for around $275 at retail prices. Apple isn't paying anything close to retail prices; they often pay less than standard OEM prices
7) It shouldn't need to be said, but Apple owns MacOS. Spreading the development cost over the systems produced leads to a likely cost of less that $1 per machine...
8) I've said it before, Apple is in a "Post PC" mentality. Killing off low margin products in the Mac line and milking as much as they can for the rest is the right strategy if you believe in a Post PC world
9) It would be more expensive (insane/stupid) for them to do that, but I can see them doing it. Why? Pride. The knowledge that their customers will pay more. Control. Differentiation. etc, etc
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Where to start. First of all, you’ve underestimated the cost of that system. The chipset for the motherboard alone is $30-40. If you’re going to claim $200, price it out. But it’s a moot point because that processor is a dead end.
If you want to give Apple system building advice, you’ve got to think about the entire lineup. What if I want decent graphics performance? USB 3.1? Thunderbolt 3? A faster CPU than 4 years ago?
The mini you envision Apple making is nothing I’d be interested in buying in 2018.
Where to start...
1) Price it out? You're kidding, right? Apple does NOT pay retail part prices. Most of the time, Apple pays less than OEM prices
2) You can build that out for <$300 at retail. At OEM/below OEM prices, yeah, it's <$200
3) Why is that processor a dead end? Really. Why is it a dead end? Ok, move to the Coffee Lake versions when they come out
4) You're seriously going to slam me for not taking a holistic view of the entire Mac lineup when there's a good chance we won't even get another Mini? Really?
5) The Mini has NEVER had much for graphics performance. Apple has always wanted you to "spend up" if you wanted that
6) Coffee / Kaby Lake supports up to 3 monitors at 4K @ 60Hz, usb-c, h265 support, ddr4, TB3, etc, etc
So... At the $500 "base" POS Mini setup, running a Coffee Lake Pentium, nearly as fast speed wise as the *fastest* 2014 Mini, with the above features, doesn't do it for you. (Note that the current fastest 2014 Mini lists at $1199 before other upgrades...)
Ok... Let's bump it up with Apple's typical price gouging...
Add +$200 for a $700 cost. Swap the processor with the i3 'T' series. Probably faster graphics. At 4 real cores, it would be the fastest Mini ever
Doesn't do it for you?
Add +$300 more for a $1000 cost. Swap the processor with an i5 'T' series. 6 real cores. Over 75% faster than any other current Mini
Still doesn't do it for you? While I doubt that Apple would put it out...
Add +$300 more for a $1300 cost. Swap the processor with an i7 'T' series. 6 cores, 12 hyperthreads. Raw compute power wise, that's more than the current highest-end iMac (not Pro and less per core)
All of those Coffee Lake 'T' series processors will have a 35W TPD, so you can just swap them in and out