Here is why Bitcoin has so much value when compared to other cryptos:

For one, it is the first cryptocurrency with the best team of developers. Being the oldest coin out there, it has managed to withstand all sorts of problems and attacks.
Compared to some other cryptocurrencies, Bitcoin has a much smaller attack surface. It has proven to be a very secure form of payment if used correctly.
So far has passed the test of time. On all major exchanges, the trading pairs go mostly via bitcoin. It is the central entity of the entire crypto eco-system.

As for intrinsic value, I think the question could equally apply to any other form of money: Does paper money have any intrinsic value? Not really. Even gold and silver
have no intrinsic value. The value is derived from people's willingness to accept and use these forms of payment as a means of exchange.