Doesn't this suggest that there used to be much less ice when the discovered artifacts were still new?

More likely that things were dropped into the snow, then covered, and remained coved in snow for a long time.

Perhaps the claim would be that the objects have been gradually sinking toward the surface with the melt.

Also, while they say vaguely that it's the least snow in memory (under a photo caption: "Domestic reindeer cool themselves on a formerly permanent ice patch (left) that melted away completely during the summer of 2018 for the first time in local memory."), that doesn't mean much. So called local memory isn't a very accurate recording. Maybe there were some other great melts across a thousand years.

Certainly could be, e.g. after the last ice age in northern europe, there was a couple thousand years where the climate there was much warmer, and large forrests covered the high mountains of what today is way above the current treeline

I just hope we find the tomb of Genghis Khan before the body is too decomposed to be conclusively identified.

I don’t understand the appeal. Genghis Khan was a fascinating individual but we don’t really need his tomb to answer any historical question I can think of (though I’m glad to be wrong.)

It would be very informative to discover the true extent of the burial goods and hints at the ceremony involved. There's a lot of lore and speculation and it can't all be right.

Isn’t it enough that he is fascinating? Would finding the frozen body of Jesus Christ not be exciting?

That would be an interesting one, as most(?) christians believe, there is none, as he ascended into heaven, so they would not believe it to be the right body, but honestly, how on earth could you prove it? (from historical evidence, it is not even clear, of whether he existed at all)

It’s an exaggerated example to prove my point. It doesn’t really hold up to any kind of analysis.

The manner of his death is still unclear (the Tangut queen killing him is conjecture)