This and similar ideas are often passed around. There are a few cryptocurrencies which try to implement something like this (finding series of primes, for example).
There are a few problems with actually implementing your suggestions. You call hashing "pointless", but it is anything but that. Hashing, specifically SHA256 in bitcoin's case, has a well understood and possibly proven (?) level of difficulty. There is no known way to gain an advantage, other than simply throwing more computational power at the problem. Thus, because the problem being solved is arbitrary, random, and difficult, it takes a huge amount of computational power to make an invalid transaction.
Not only do you have to find initial "acceptable" hashes for your faked block, you have to create hashes of all the following blocks up until the present time, and push this version of the blockchain as legitimate until a majority of the network adopts it as the correct branch. The absolutely ridiculous computational power required to do this is what keeps transactions of cryptocurrencies safe. You don't just have to fake one hash, you have to find and fake an entire chain of them!
Many scientific problems don't have the same kind of guarantees about difficulty. And even if they are really, really hard, what happens when you find the answer? You'd essentially have to hard-fork all the clients. SHA256 and other hash functions used have a search space that is astronomically high, and is guaranteed never to be "completed".
Hashing is a way to make transactions safe, permanent, and unmodifiable because of the cryptographic properties which come with the field. There's very little chance of someone stumbling upon sequential solutions, and essentially impossible for someone to "derail" the blockchain due to those properties. The value that hashing provides are those guarantees.
This is why I'm just throwing the idea out there (though, as you say, it's probably not even a very original one). It would take some thought to figure out a way to make it work as well as the current hashing system. Perhaps "pointless" was a careless choice of words, but the incentive is to put all those cycles to a use that had more value for society, apart from the value of creating bitcoin itself. I forget the exact order of magnitude, but iirc it's something like tens of millions of dollars of electricity being used by miners each year, for no other purpose than to verify the blockchain. It'd be convenient if we could still have cryptocurrency, but all the computing power was going into something like BOINC instead. Hashing is used for good reasons, as you point out, but it's a wasteful use of resources, in my opinion. Even if it wasn't the best cryptocurrency, something that would crash and die with new scientific/mathematical advances, I'd still consider it successful if it got all those resources working on more valuable problems for a while.
It's definitely a half-baked idea. I'd like to take a shot at seeing if I could work out those details, but it's not the top priority on my list of projects. Maybe in a few years, if it is possible and no one else has managed it yet.
There are a few problems with actually implementing your suggestions. You call hashing "pointless", but it is anything but that. Hashing, specifically SHA256 in bitcoin's case, has a well understood and possibly proven (?) level of difficulty. There is no known way to gain an advantage, other than simply throwing more computational power at the problem. Thus, because the problem being solved is arbitrary, random, and difficult, it takes a huge amount of computational power to make an invalid transaction.
Not only do you have to find initial "acceptable" hashes for your faked block, you have to create hashes of all the following blocks up until the present time, and push this version of the blockchain as legitimate until a majority of the network adopts it as the correct branch. The absolutely ridiculous computational power required to do this is what keeps transactions of cryptocurrencies safe. You don't just have to fake one hash, you have to find and fake an entire chain of them!
Many scientific problems don't have the same kind of guarantees about difficulty. And even if they are really, really hard, what happens when you find the answer? You'd essentially have to hard-fork all the clients. SHA256 and other hash functions used have a search space that is astronomically high, and is guaranteed never to be "completed".
Hashing is a way to make transactions safe, permanent, and unmodifiable because of the cryptographic properties which come with the field. There's very little chance of someone stumbling upon sequential solutions, and essentially impossible for someone to "derail" the blockchain due to those properties. The value that hashing provides are those guarantees.