Stablecoins have been considered among many investors to be a safe-haven for crypto's volatility. Ever since Tether (USDT) emerged, several other stablecoins have launched in order to provide people with a wide variety of options to choose from. However, the stability of stablecoins is yet to be questioned since we've seen how Tether has gone below $1 in the past.
NuBits used to be a stablecoin too, but now it has lost its peg to the USD. Which means, that the same thing could happen with most stablecoins out there, since they're traded on a free market.
Nonetheless, do you believe that stablecoins will have a future? If not, why?

Stablecoins are not going anywhere, it will stay as long as cryptocurrency stays and crypto is a forever thing.
As you said stablecoins are safe heaven among many investors and it is 100% true. Investors need such stablecoins and they can't ignore it.
Tether has gone below $1 and it has also gone to above $1. I have seen $1.03 max so far and with a low of $0.94
You may also include traders who tend to trade a lot. As the market condition is quite bearish or the volitality is too high, they need stable coins such as Tether for their exit trade; these stable coins are keeping them losing for such market that is unfavorable for them.