If you are testing the conversion rate in shopping carts, and the changes involves drastic redesigns of the flow through the shopping cart process, that could be a serious technological difference and requires substantial time to implement.
Not every test is as easy as changing the copy on an email.
In other words multi-armed bandit versus A/B test is something that you shouldn't be deciding based on the effort of the testing methodology.
That's how I interpreted his statement. I agree with you that the actual A/B testing overhead should be minimal and fairly trivial to put into place.