I understand that since altcoins are paired with BTC for trading, the price is based off bitcoin's.
However, even if an altcoin is doing well, it can tank (in terms of sats) when bitcoin's price corrects.
Will we ever see a market that isn't so heavily dependent on bitcoin? Is this possible for the future?
Probably it will be possible in future. However, as you noticed BTC is the main pair traded at criptocurrency exchanges and altcoins depend on BTC price