Why would I want to build more floors?

Solution 1:

Some missions payout more chips the more floors you have. When your mission is to find something (objects or bitizens), you get one chip for every 20 floors you have.

So floors 1-19: one chip
Floors 20-39: two chips
Floors 40-59: three chips, etc.

In addition, while floor costs increase logarithmically, the floor tip bonus increases exponentially. It's not a huge money-maker, but it can help bring in coins short-term.