Absolutely. That's my biggest objection to bandit methods, but it's also the fuzziest objection, and the one least likely to appeal to hyper-analytical people. There's a strong temptation (as we can see from this article) is to treat bandit optimization as a black box that just spits out an infallible answer (i.e. as a Lazy Button).
It's the same human tendency that has led to "you should follow me on twitter" to be one of the more common n-grams on the interwebs (even though it probably never worked for more than Dustin Curtis, and likely causes a counter-intuitive backlash now).
Of course, these algorithms are cool in certain contexts where you never want to think about it again. For example, ad placement for a giant ad network running against a lot of UGC content. They remind me of neural networks like that: the post office doesn't care how the machine recognizes hand-written zip codes, just as long as they do it reliably.
But startups are all about learning, and interface design is where you have direct contact with users. I want to soak in the data. I want to hang out in people's living rooms when they're using my site. A fancy Lazy Button (great phrase) is the last thing I need.