If we compare the crypto assets market to the stocks markets in general, can Bitcoin be considerated as the equivalent of the dollar?
In the stock exchage we buy shares with dollars.
In the cryptocurrencies exchanges we buy tokens or coins with bitcoins(and other cryptocurrencies, Litecoins, etc).
Even though I don't really believe in the comparison you're making (I think there are a lot more benefits to cryptocurrencies that you leave out as well as some downsides), I wouldn't really consider the dollar to be a bitcoin equivalent. With fiat currencies, there isn't one "central hub currency" that you can always use to get all the other currencies. If that was the case, that main currency would be worth way more. Bitcoin is like the major currency that you can use to buy other currencies and that often can drive the price up.