Setting up a new kitchen

Where are you?

When can you expect deliveries? Everyday? 3 times a week, once a week?

Storage space is not dictated by the menu - it is dictated by how you cook the menu.

Cooks can prep on the the line if given the right space and time. If you are serving 24/7 then you can't use the line obviously.

Work the menu and method to the space you do have ... unless you have unlimited funds.  Then build a place to fit what you want to do.

A walk in full of wine and cheese at a white cloth table French / Creole Brasserie, never would have guessed that one.

The menu should be built around the kitchen, not the other way around. Small kitchens mean small menus if you want high quality food. As already mentioned, delivery frequency is also a big consideration with small kitchens. With only one small walk-in, I would want delivery at least 3 times a week.

It would be easier to give a strong answer if I knew what your partners like about the location and how they feel about the small kitchen. The other chef must be able to see the limitations you describe. Having been in a similar partnership for many years I suggest an open, exhaustive (and exhausting) discussion with your partners so you can outline your concerns and they can respond. Throughout this discussion, logic,not emotion should be your guide.   As the others have pointed out, size influences a number of considerations, not the least of which is possible future expansion. Is the building lot constricted permanently or could there be opportunity to add on at a later date, whether that addition is dining, kitchen or parking? How much money do you spend on what, now or later? What will affect the restaurant most will be the relationship you have with your partners and an open, honest discussion about everything now will reveal how well you can listen to and respect each other.

You will get your way sometimes and other times you will have to suck it up and live with what the others want. Or as my father told me once "You can be right all the time or you can be in a relationship, not both". 

Having said all that, the more room the better for me. I've done small and large, large is better for everything from prep to cleaning up. But good design will help mitigate the lack of room.