Why can't there be a normal P2P project handling exchange of information and/or modern fiat in the same way (Something like Paypal, but transactions have no middleman)?

Firstly because money is a physical, cultural and social construct so it can't be changed on purely informational basis. Someone still need to share burden of proof and they want to be compensated for the labor. So until we get a StarTrek replicators (mean we remove need to spend money on basic need and survuval of whole human race) this is a state we are in.

In short blockchain and crypto don't solve any real world problem. It solves problem that it itself creates.

I can sell you amazing knife and it will fix the world hunger, but only if you can buy bread and sharpen the knife. This is crypto sell point in the nutshell.

Blockchain is little different as it solves the problem of provable chain of evidence, but it is not economically viable due costs needed to run it for organisations that require it. Any problem that blockchain can solve require that all information for this will be stored on blockchain. And physical object information is not stored on blockchain, so data input errors/malpractice is still the problem and this reduce blockchain effectiveness to the basically zero.

Dan Olson aka foldablehuman have an amazing series of video essays regarding all the crypto blockchain and web3 scam running around. I highly recommend them. It just a sea of information regarding current state of things with crypto/blockchain business.