but it can replace the current internet payment systems, instead of paying with credit card over the internet that will also require you to reveal your credit card details, you can play anonymously with bitcoin.
I highly doubt that. People nowadays are too dependent on credit to sustain themselves, so the fiat related payment infrastructure will remain pretty much for ever and beyond, thanks to this shitty system.
Also, in order to spend Bitcoin, you have to buy it first, and let that buying happen through centralized services, which basically means that the anonymity you're referring to doesn't exist.
Mixing could be an option, but mixing services are still a niche in current days, and as long as that doesn't change, people will not be able to obtain even a remote form of anonymity. Blockchain = big brother is watching you.
Credit cards and fiat money will never disappear, maybe will just change forms. Bitcoin has shown the world the potential of crypto-currency and blockchain but it just might as well remain an investment asset.
That's why we see that, more and more, countries and various private businesses are developing their own crypto. That's unleast how I see the future of "future" alt-coins. They'd be developed as a kind of "coupons" that you an cash in for various cost deductions or whatnot, therefore that coin will remain within the business.