There is a limit to how many GPU chips can be pumped out by AMD and Nvidia due to LIMITED FOUNDRY CAPACITY on the production nodes those chips are made at.
They are also competing for that capacity with OTHER THINGS, like AMD CPUs and Samsung smartphones and Apple smartphones among MANY OTHER high-quantity selling items.
Keep in mind that ONLY AMD makes the GPU chips for AMD brand cards, and ONLY NVIDIA makes the GPU chips for Nvidia brand cards.
It's NOT up to the likes of EVGA, Gigabyte, Sapphire, ASUS, MSI, et cetera, as to how many cards they CAN make - if they don't have the GPU chips, they can't make the cards.
Gamers have been able to buy cards - they just didn't always have the option to buy low-cost midrange cards for cheap the last few months. I suspect that gamers "moving up from the 1070 to the 1080" due to shortages of 1070 cards and gouge pricing had a lot more to do with the MINOR availability and pricing issues of the GTX 1080 than miners have had, and it's noteable that the pricing of the GTX 1080 ti never moved noticeably even though availability got a LITTLE spotty on occasion.
BTW - this is also why Bitmain (and others to a lesser degree) have been often OUT OF STOCK on miners - they are SMALL FRY compared to the big boys, and have a much harder time getting ANY access to foundry capacity at all on the current "state of the art" nodes they're mostly using for the current miner generation.
Contrary to your assumption, they CAN'T just "max out their production" because the chip makers are ALREADY running flat-out and have been since the 14/16nm nodes first hit production status (less a short interruption of TSMC when their current-node factory got hit by an earthquake and lost ALL production for a couple months or so).
One additional factor for AMD - they got HAMMERED a few years back when the Litecoin/X11 GPU mining craze died, because they sold too many cards into the craze only to have the market dry up BIGTIME for a good year after that collapse, due to oversupply of cards on the used market. They seem to be trying to avoid that to SOME degree this time around by (1) encouraging their AIO partners to come up with "mining specific" cards that won't drag the market down for "real" cards much if at all, and (2) NOT ramping up production to crazy levels (even if they COULD) to try to keep up with the short-lived demand at the cost of the long term ability to KEEP SELLING CARDS once the current demand dies back down again.
One more point to keep in mind - demand seems to have ALREADY leveled off or dropped some due to ETH (and ZEC and some degree the other GPU mineable altcoins) having major profitability drops over the last couple months, pricing has already dropped a LOT vs the peak and availability is starting to recover quite a bit as well. NVidia is still seeing some elevation on 1070 pricing (and probably on 1060 pricing as well) but it's not CRAZY high any more, 1080 pricing is pretty much back to where it was in Febuary before the craze hit, and RX 570/580 card pricing has dropped a LOT over the last month though it's still elevated, while availability has improved a TON vs a month ago.
The craze isn't over yet, but folks are obviously starting to have second thoughs now that the potential for "2-3 month ROI" is dead and there appears to be some potential for "never achieve ROI" on the horizon with the ETH plans to move to POS actually ROLLING this time around.
Care to enlighten us where these lowered price RX 570/580 with TONS of availability are hiding? LOL Newegg has actually RAISED the prices on RX cards by about 10-20% over what they were a month ago and is completly sold out except for overpriced open box cards. Another thing we learned from the Scrypt GPU run-up from 2014 was GPU prices were quick to go up, but slow to come down until long after mining profitability was non-existent.
