E-commerce sites want to "engage" with their customers, but fail to realise that the customers don't want a relationship. They just want whatever product you're selling as quickly and cheaply as possible. Most of you customers will be coming via price comparison sites or Google, so they aren't going to you directly (unless you're Amazon or eBay). For most e-commerce sites the customers aren't going to stay long enough to notice imperfections in the UI.
What you do need is a dead simple checkout (no signup required) and an equally easy return form. Everything else will be used by only a tiny percentage of your customers, often those you don't want to deal with anyway.
For some weird reason making the checkout to simply will result in a large number of purchases cancelled right after placement. In my experience customers are more likely to cancel within 15 minutes of placing the order than at any other time.
These two statements are contradicting each other, because "imperfections" in the UI can in fact greatly affect the perceived simplicity of the checkout process - and optimizing that is a large part of what people want to achieve with A/B testing.
I have done a/b tests where increasing the price of the product increased the conversion rate. The original price was to low and the customers thought this was a cheap non quality product.
Also I, and many people I know, are not shopping for the lowest price, but for the best overall package. (Reputation of seller, return policies, shipping duration, display of the product in the shop, filter and search abilities to find the right product in the shop, ...) There are of course many users who simply want the lowest price, but one important thing if you a/b test is: You don't have to go with the biggest group of users (in this case price sensitive), there are so many other oppurtunities if you understand your users. In e-commerce these oppurtunities open especially often, if the user is not exactly sure what product/brand he needs or wants to buy. Competing on price is really hard, competing on advice is often easier as a small shop.
What you're selling sets the threshold for those things. Return policies, advice and reputation matter more for embroidered clothing than they do on bulk sales of nuts and bolts.