Not at all, how that price is built up is extremely relevant. If an item is cheap but shipping is horrendously expensive, I go look if I can find it at another webshop that has more reasonable shipping. Shipping is part of the total price. Pretending it's not is taking information and choice away from the customer.

There are exceptions to this. For example, I trust McMaster-Carr to charge me whatever they get charged for shipping, which is good because they won’t tell you in advance what it will cost. But in general it’s just another number. It’s a really common scam to have a cheap item with expensive shipping in order to trick people who aren’t paying close enough attention.

Put it this way: store A is selling widget X for $40 with “free shipping,” store B sells it for $35 plus $5 shipping, and store C is $15 plus $25 shipping. Who do you buy from?

For example, if C sells something else that I want that's also much cheaper than a the other shops, and it won't increase shipping costs much, then that's the better option. If not, I may continue to shop around until I find a shop that combines low item price with reasonable shipping cost.

As you say, your store preference depends on various factors. If C’s shipping costs are structured one way, you’ll prefer them. Another way, you won’t. You have to know all those details before you can choose. That’s my point: ultimately, functionally, there is no difference between a random store that won’t show you prices until you give them your location, and a ransom store that shows prices immediately but won’t give you shipping costs until you give them your location.