Why is the Zcash to BTC value always relatively stable since its inception,
it is because you are interpreting the chart wrong! you have zoomed out too much that you are also including the fake initial price that was gigantic (1 ZEC = 8.34 BTC) and everything else is dwarfed compared to that! so it is creating the illusion of being stable.

but if you change your zoom and also look at the values you can see that there is no difference between ZEC and any other pump and dump altcoin. it had its own pumps and it is like other altcoins, on a general decline losing its value over long term. in the past 3 months alone it has lost half of its value:
