The fact is that Bitcoin Core as a wallet is not a big application. It's a full node which means once you install it and it's running on your computer, it will help with the validation and transmission of other transactions on the Bitcoin network and will save a copy of the entire blockchain on your computer... That's why you think the wallet is big in size, but instead, it's the whole blockchain data saved in there.
The advantage of this wallet is it brings in better privacy since it won't rely on peers or external servers to get data.
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I want to know what people will do when Bitcoin's wallet size reach 300GB or bigger.
Solution to the Size problem is to;- Store you blockchain data on a separate Harddrive, but always ensure it's mounted when you run your Bitcoin Core
More details here:How do I relocate my bitcoin data in bitcoin-qt to save space?
- Use other lighter wallets like;
More information about Thin Client Security
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If someone invents a new kind of digital currency that won't come with such downsides, what will happen to all existing cryptocurrencies?
There have been over thousands of cryptocurrencies (2072 coins/tokens are officially listed on coinmarkecap) introduced with an attempt to overtake bitcoin in the number one position in terms of market cap and adoption but none has succeeded to this date, so, "What will happen to all existing cryptocurrencies?" I bet your guess is as good as mine