Why the Evas have physical inputs?

[AyrYntake]

Plug depth...that's an interesting one. I always thought plug depth was controlled mostly by the NERV bridge bunnies from the outside, but I guess the pilot would have some say over that as well. Then again, when Mari goes THE BEAST nothing shows her using any of those controls...could all be implied I guess.
Then again, it's not just plug depth that controls synch ratio, of course. We know that the interface headset does something, and so does the LCL. The control sticks could be an equivalent to a volume amplifier slide for the interface headset, or something like that.

[simonmagwitch]

Then again, when Mari goes THE BEAST nothing shows her using any of those controls...could all be implied I guess.

It could also be a function of THE BEAST mode. Didn't she increase the plug-depth past safe before Maya stopped being able to monitor the plug?

[AyrYntake]

She did, but nothing shows her pushing the control sticks is what I mean.

[berto]

Well, as Ritsuko said, that mode isn't something that have a lot of risks. To go that deep into the Eva is rather reckless so it's provably better to not try to synch with an Eva too well, just ask Shinji.

[AyrYntake]

I know it's a big risk, I'm just saying that the exact role of the control sticks in synchronizing with the Evangelion is unknown.

[berto]

We should also consider the notion that it's just there for estatic purposes. It might not have any other use than to look like it belongs.

[The Fourth Evangelion]

There was also this scene with the second angel, in which Shinji stabs it. EVA-01 is seen stabbing the ngel with both hands. Shinji does excactly the same, with his left stick. So, I think they serve a function

[Baz]

I like to think that the handles are used for precise control of the Eva's hands. In humans (and other apes and some monkeys) the hands and forearms are wired directly to the primary motor cortex, while control of other muscles is indirect i.e. the primary motor cortex gives the walk signal, and then other, older parts of the mammalian brain take over. So it would make sense that the Eva's would require a direct control system for the hands/forearms while control of the rest of the body is "emotive".

The hand controls don't seem to be very precise, though. The fingers cannot be controlled individually with them. All the pilots can do is reach and grasp. And pull triggers.

[AyrYntake]

NOW we're talking science...well, pseudoscience at least. Perhaps, that being the case, the control sticks are in a sense there to provide assistance to the PMC's signalling?
From the LCL injections to the insertion of the entry plug into the brainstem, not to mention the mother-and-child relationship, everything about the connection between Eva and pilot screams primordial. As you said, walking is controlled by parts of the brain that evolved earlier than the PMC, and as such is probably easier for an Eva and its pilot than, say, complicated forearm and hand movements.
Seeing as one of the most important foci of a humanoid weapon are these very movements (trigger pulling, punching, grasping a knife and stabbing etc.), the NERV staff must have thought it reasonable to install handles for the purpose of amplifying or clarifying the signal sent towards the forearms and hands. Sure, they may not be precise or detailed, but they may not need to be: a strong pulling or pushing action may simply send the message for muscles to contract more forcefully, and pulling the trigger, well...pulls the trigger.
I doubt, of course, that Anno and his team went as far into this during the design stage as we have, but it's all harmless fun I guess.