That would be one single point of failure and one single target for attacks - fully centralized and extremely vulnerable.
Plus, the amount of people entrusted for caring about that central spot would be pretty small and the risk of any of them grabbing or manipulating the jackpot & run off would be extreme.

ergo -> extremely bad idea

The more decentralized, the better, stronger and more reliable it becomes, because it needs to survive successful attacks and temporary deficiencies/technical failures of all sorts.
After all, it's a very greedy humanity we're witnessing right now, thieves and scammers of opportunity are literally around every corner.
Additionally, everything used in the process is typical, off-the shelves hardware which will occasionally malfunction or fail at some time and require periodic maintenance/upgrade downtimes.

And when it comes to new coins.... *ugh*.... we already have more clones than anyone would ever need.
A truly new one actually improving and erasing all known and projected SHA256/Scrypt weaknesses or risks is nowhere to be seen.

This is what P2Pool is.

Yes P2Pool does pretty much what you want.

However hashers are slightly more financially incentivized to use the larger pools.

Incentivising Hashers to use P2Pool is imo the most important thing Bitcoin should be doing right now.

+1

P2Pool