Most jets have a shut off valve to use in an emergency & there was some discussion in another thread on whether the valve should go on the suction or discharge side of the pump.
The main objection to the valve being on the discharge side of the pump was the valve & fuel lines would be subject to the considerable pressure fuel pumps are capable of generating & the risk of a line or fitting bursting spraying fuel everywhere.
With what you are proposing the entire fuel system would have to withstand this pressure.
As Jason said, a lot of work has gone into the current system & the bugs are pretty well ironed out, lessons learnt the hard way mostly.
But new ideas are always welcome!
Since I'm new to turbine-powered airplanes
Welcome to jets! - John.