Are there negative consequences to ignoring a floor type when adding floors in Tiny Tower?

The Food floors are just an annoying time-sink for me. They are constantly out of stock, and floor upgrades only add minimal inventory. Ideally i'd never build one, but I'm content with just waiting until that's all that remains.

Are there any negative consequences if I hold off on building Food Floors until I have no other option?

You will see a severe decrease in demand for all non-food businesses (which applies to ALL businesses of that type, not just the extra ones) when you fail to keep businesses even. The demand % you see directly relates to the amount of people that will visit each floor of the type. At 100% demand, each floor gets 10 bitizens (purchases) per minute, each 10% demand drops, you lose another bitzen/sale per minute. The drop in sales will be substantial.

From the Wiki:

demand = total commercial floors / ( 5 × total category floors )
A floor of a lower demand category will draw less customer traffic than one of a higher category. For this reason, it is beneficial for the player to keep demand on all floor types high by building from each category evenly. The following table illustrates the approximate impact of various demand levels.

Thanks to demand, it's better to have food floors you just don't stock than to not have them at all, so just buy some food floors, you don't even have to stock/employ them. You can spend a tower Buck per floor to shove all your food floors together and ignore them as a set if you wish.

If you don't put employees in your food floors, you can save some bitizens for your other floors, thus needing less residential floors per commercial floor. Residential floors don't affect demand.

One minor side effect if you don't build any food floors is that you'll run out of floors to build earlier. There is a limited number of floors of each type (19 for each store kind and 57 residential, to a maximum of 153 floors, as of version 1.5.1), and once you build all type variations, you won't be able to build any new floors. So if you ignore food altogether, for example, you can only build up to 134 floors.

This issue, of course, won't be encountered by most of the players, since reaching this height will take several months of playing.