Yes there are options, but if sites can store billing information, they can store shipping preferences. They can pick a reasonable default.
In fact, they already have all the necessary information, you can tell by the way some online merchants will have a single price in bold, then below that in fine print +$x shipping + $x tax, like so: http://imgur.com/krReEkz
They just don't have any interest in advertising more accurate (and thus higher) prices than their competitors.
They know the numbers, there's no reason to hide the final price here, except that the competitive market is forcing anti-consumer behavior.
On one hand I just wish they wouldn't list marketplace sellers when they already stock something themselves. But, doesn't having all those other options (as imperfect as they are) sway things a little in the consumer's interest?
Your reply: "I'll buy items stocked and fulfilled by amazon"
My next post: (Me too, my point wasn't really about Amazon.)
Your reply: "this isn't a problem unique to amazon" (and your evidence isn't even from amazon, so that's a strange way to make a point about amazon!)
Me: ಠ_ಠ
I get it, you're trolling me. Very funny.
I guess that would be difficult when there are several shipping methods being utilized. If I buy an item stocked by amazon I'll usually get it the next day via amazon logistics, DPD, or royal mail (when I'm in the UK).
If it's a marketplace seller it could be royal mail first class, royal mail signed for, royal mail 'wish upon a star' class or, if I'm really unlucky, some random 'gig economy' courier.
That's an awful lot of options to weigh up and most of the time I get no choice in which will be used.
Like someone else has commented, I'll buy items stocked and fulfilled by amazon, whenever it is an option, and I don't care if that means I pay a bit more.
Buying cheapest usually costs you more in one way or another.