I'm not sure this will actually bring down prices. There's still a limited amount of chip production capacity, and every individual mining-unlimited chip which is produced means one less LHR chip being produced. So supply is still restricted by production capacity, and demand is still being increased by mining. Splitting the cards into two product lines will not, by itself, affect either supply or demand for the silicon chips. Remember, at root, gamers and miners are both demanding the same chips from the same production line. The LHR is a small tweak that doesn't fundamentally affect the supply of what are otherwise identical chips.
It's like Ford taking a blue car and splitting it into two production lines: a blue car and a green car. That won't by itself affect supply in any meaningful sense. The two cars still compete for the same production capacity.
Miners will still be willing to pay inflated prices, and if chip production capacity is diverted from the LHR line to the mining-unlimited line to serve mining demand, then prices won't actually fall.
Now, it's possible that Nvidia will focus production on the LHR cards to reduce their price for gamers and free gamers from competing with miners. If Nvidia devotes more production capacity to LHR chips than mining-unlimited chips, then prices for gamers will fall and prices for miners will rise. But it's not clear why Nvidia would do this. Why sacrifice revenue from high-paying miners? Perhaps to retain the goodwill of gamers in the long-run, after the mining craze is over?
My guess is that this is just an attempt at price discrimination. Same way that the same chips are repackaged as low-end (xx30), middle (xx60) and high (xx70, 80, 90) at different price points. Different people have different willingnesses to pay. Artificially segmenting your product allows you to charge each person an amount that approaches their maximum willingness to pay.