On a given map, the Dig Sites grow increasingly more expensive as the player progress. However, the artifacts don't seem to improve at all. The first few Dig Site encounters may only costs a few hundred millions, but the artifacts they produce are on average about the same as the Dig Sites encountered later, which may cost trillions (or more). I find myself spending a significant amount of money on Dig Sites per game, and imo there should be some correlation between the price of the dig vs the quality of the artifacts. It makes little sense to spend a trillion on a dig sight for 100% common in the late game, as compared to spending only 100 mil on a 60/40% uncommon/common artifact in the early game.

Numerical, you are correct; however, the value of 'money' late in the game is very different than the value early in the game. When you 'earn' only a few thousand per second that money has more value than when you earn 100's of thousands per second not to mention the value of selling items. Early in the game a 100K dig seems expensive, but when you sell a single item for many billions, the cost of those later digs is not so much.

There is a corollary in real life as most of us age, we earn more (even when accounting for inflation) to the point where what were extravagances in our 20's are now 'little luxuries' later in life. IMO.

Artifacts rarity and drop rates doesn't change depending on map or map stage where you find excavation sites.

I've found, there is some correlation, though, for rarity and digging time. But for the cost, everything is said. If you feel it is too expensive for your wallet, you can always only dig the first site per level.

Although, I have to say, I would, too, expect rarer digs both the higher the costs and the higher the level, but that isn't really the case at all. Even in levels above 15 (so far) 50% of the digs are straight commons. Sure, the more progress you have in some level, the less important is some specific amount of money but being able to spend a higher digging cost also means that you already invested some time into this level, so why not reward the player with rarer artifacts the higher the costs are.