RE: As goes BTC, so goes the market.
Not only is Bitcoin a household name but it also is the largest in terms of market cap which make it the number one store of value among the cryptocurrencies. This will solidify its position in driving the sentiment of the overall market. Although BTC dominance has dropped considerably it also continues to be a barometer of the market sentiment as many hold Bitcoin before entering other crypto positions. Therefore, Bitcoin price could be a conundrum in certain cases. Surely, overall bullish sentiment will bring up BTC and the other altcoins but we have seen that it drops BTC dominance as well. This is likely because of people selling the BTC pair of altcoins on exchanges and many assets out of the top 5-10 do not have direct gateways with fiat currency. However, in the long run we will most likely see less correlation to Bitcoin as altcoin “sectors” become more specialized like platforms (i.e. ETH, EOS, etc.), payment processing (i.e. LTC, XRP), privacy coins (i.e. Dash, Monero, etc.), Decentralized Exchanges (i.e. ZRX, BTS, etc.), among others that continues to be developed. This will lead to sectors performing in uncorrelated ways to each other given the adoption and performance of their protocols individually and the demand for their sectors.
I see sectors developing in much the same way that you mention, and as direct gateways develop, that too will help Alts gain independence. It's still very much one big, very interrelated and highly correlated market though, and likely to stay that way for some time. There was a time when there was an inverse correlation that I was expecting to come back someday, but now I'm thinking that's getting less and less likely. Probably more of the same, and a slow process of independence.