I don't think ETH needs to have the same price as BTC. While BTC is a store of value for many, ETH is very different. And its use is more universal. Websites, games, NFT and more.
Ethereum network being web 2.0 is having smart contacts on it which can make anything possible whereas bitcoin as you said is used just for storing a person's money and nothing else. I guess ethereum was never invented to compete with bitcoin, if bitcoin is the king of cryptocurrencies then ethereum is what bitcoin blockchain is missing and make the crypto world more robust. Cross chain transactions, smart tokens, wrapped tokens and many more being present on the ethereum chain make it superior to BTC but still it won't surpass the bitcoin price just because of the limited supply of bitcoin and ever increasing supply of ethers.
Yes, that's right, there are too many functions for the creation of bitcoin for the community. Apart from being a store of value, bitcoin can also make it easier for someone to make transactions, as well as ethereum and other potentially cryptocurrencies. I agree as you said that ethereum was never created to compete with bitcoin. this is very interesting i think