Take-off flap B737 Classic
 

Can anyone advise why the 300 is designed to use flap1/5/15 for take-off as appropriate, while the 500 is designed to use flap 5/15 only.

We use Flap 1 for improved climb situations on the -300, can't shed any light for the -500 though!

In a nutshell because that's all that Boeing provided for the certification package.

Seriously, though, certification is an expensive business. Unless there is either a general demand for a facility amongst the buyers (ie the facility is provided or the lack depresses demand for the product generally), or the OEM foresees a marketing opportunity in providing an option, it's not going to happen, regardless of whether it is feasible or not.

This is no different to what a mouse trap manufacturer provides in the package on the supermarket shelf.

Boeing is in the game to make a dollar for its shareholders, not play altruistic provider of freebies.