Rainbows themselves don’t suck; I’m a big fan of actual rainbows after rainstorms as well as the Muppets’ song. But when you try to work rainbows into a logo or a repeating graphic, they are problematic because you’ve left no ground for contrast. What’s the big deal about contrast?
Let’s look at the most contrast, black and white. You can easily see that black vs white is easiest to read.
Each color in your rainbow is either going to act more like black or more like white. Pretty simple, but you may not have thought about it! You can see that no color of text will work across the rainbow.
This is a simple example — that of enough contrast for readability — but the lack of contrast will haunt the design. For example, if you want to use a color to bring attention to an important reminder like “Parking takes Cash Only,” you will have used up the attention-getting quality of all the colors. Creating categories also requires contrast so you’ll be hindered in trying to establish relationships between headings and different lists.
If a rainbow is essential to your brand, this tradeoff might be worth it. But hopefully knowing it will limit your options will help you decide if rainbows are for you.