how possible/feasible it is to build/run a centralized exchange with full non-custodial wallet system implemented?
If centralized
only means there's a place (usually website which controlled by a group/company) to meet buyer and seller, it's possible. But people usually call it P2P rather than CEX even if both buyer and seller need to use that website. Otherwise, i don't see how it's possible on technical level.
Yes; this sounds to me a bit like
Robosats. It's a centralized (onion) platform, but buyer and seller trade P2P and get their funds directly into their wallet. I may write a review fairly soon, in case anyone's interested. Anyhow; I noticed that the funds to sit in the service's wallet for a short amount of time, as it acts like an escrow. I don't believe they charge fees, but it would be possible to build something similar with a built-in fee, for sure.
For some inspiration, I'd encourage Fivestar4everMVP to just try it out once.
There's also
this walkthrough that you can have a look at.
Another concept that I keep bringing up, which doesn't hand custody to the service, but instead uses multisig transactions is obviously
Bisq.
My 2 cents about the opening statement: I found it funny how your main motivation seems to be 'building a very big business' and 'being a CEO to a big crypto currency exchange', instead of - I don't know - 'building a useful service' or 'creating a privacy-enhancing service', or maybe 'building something that helps Bitcoin'..
Sometimes, the best ideas come when you're not 'trying hard' to 'become a big CEO' or something like that; best example is satoshi. He wanted to create a trustless digital cash system, achieved it, and disappeared; probably gained little to nothing personally, but changed the world..
On the other hand, the modern-day altcoin creators are mostly scammers just out for 'big CEO' status and making lots of money quickly.