The value of altcoins is tied to Bitcoin. In other words, if Bitcoin goes down 10%, most coins go down 10% as well.
You can mine multiple coins with a SHA256 miner (Bitcoin).
The point about weight and what's available you is the most important in your case.
I think since BTC was the pioneer of cryptos, you're right that for the most part, altcoins have only managed to get any value by riding on BTC's coattails so to speak. That said, BTC confirmations are taking longer and longer by the day, and no matter how many server farms we dedicate toward mining, that is only going to continue being the case. For people/wallets that are paying low miner fees when they make a transfer, it's already not really viable.
Plus, the blackhats that made BTC what it is today are gradually becoming less and less trusting of BTC due to it's not-as-anonymous-as-originally-purported nature, and they will begin to back a more secure/anon crypto (Monero, most likely). Mine Monero.