Same for me, i use a PSX dual-shock which is an analog gamepad
with 2 joysticks. I just CAN'T apply throttle while i brake anyways.
I did try to assign brakes to the left (y+ axis) while leaving throttle on
the right (y+ axis), but steering is on the left joystick (x axis) so it
means i have to compromise braking when i turn and vice-versa. Not good.
It WAS different and kinda fun for a while, until you need to brake and turn
at the same time...
Because of that, i leave auto-blip for downshifting (else the powered
wheels lock up on downshifts) but i deactivated the auto-cut. I manually
let go of throttle when i shift, like in realife. It feels more natural after a while
and yes, there IS a very small advantage if you keep throttle on
while shifting, although i can't 'flatshift' in any car without dmaging the engine,
i do apply throttle a bit early, which gives the same advantage. So far,
only guys with actual pedals (including clutch!!) and shifter seem to be
able to shift faster.
As i've mentionned on other posts, i kinda HAD to do it once i realised
i'd never win a drag against people who already do this. You can hear
the rpm raising between their shifts, sounds a bit like someone slipping the
clutch. On a road course it's a small advantage, but on the drag strip,
it can amount to 1-2 car lenghts at the 1/4 mile mark ! You just lost there.