But being that a product can be the first of its kind to be made (just like Bitcoin) and other companies may decide to produce similar product;( just like alts) but that doesn’t mean the original product price and value will always affect others. So why does Bitcoin have such a big influence on other alternative cryptocurrencies.
Going by your example of a product and it's alternative. It does not hold same for bitcoin. But I will try yo use the product name to explain to you why bitcoin leads and others follow.
Let us use Coca-Cola company as example. Let us say that the Coca-Cola company is the cryptocurrency, coke is bitcoin while other Coca-Cola products are altcoin. If coke is banned, the Coca-Cola company sales will drop drastically even if other drinks are available. Coke is the mother and face of Coca-Cola, but if coke is banned, it will not affect the peak milk company because they are not related.
Bitcoin is the mother and father of cryptocurrency, if the parents didn't provide food, both the parents and the children will starve.