The reason, is the value people see in products.

You can build a pc yourself, equal to the steam machine with random parts online, from shops for like 550$.
You cannot build a handheld yourself, from random parts online.

This is why.

The markets decide the prices, by the competition surrounding them.

People are okay with paying high prices, if the perceived value of what your buying is there.
Its not with the steam machine, if you can build something yourself equal in power for like 550$. 

Also with handhelds, a huge part (of the price) is the battery and displays and speakers and such....
stuff you don't need to care about in a console/mini pc. 

It's about $150-$180 for screen and battery replacements according to iFixit depending on which one you choose. I think the boost in power surpasses that kind of price.

The price of the replacement parts for the Steam Deck isn't that much, so that doesn't seem to be much of a factor in perceived value, but then again, how much of the public are gonna go to iFixit to get replacements parts lol

I don't think the Steam Machine should be priced more than $600 at the very most for the base model. Preferably $500, but, we also don't know how much things like tariffs and the massive increase in RAM prices recently will affect the final price.

I still think it will sell well at 600$.
700$ will be pushing it..... sales will stall, because I think most pc users, will build themselves if it means they can save 100$.

Newegg pc, sold Prebuilt :

i5-13400F + RTX 5060 + 32GB RAM + 1TB NVMe M.2 SSD + windows 11
Comes in a small tower:

^ this is 870$ and  much more powerful than the steam machine is.


There are 100's of PC's like this, around this price range at various sites selling prebuildt pc's.

Why should Valve get to charge anywhere near this for its steam machine?

It shouldn't, and consumers won't go for it.

Otherwise I would guess a 699 or a 799 system, but as a realist, it's 899. The cheaper model may be under 800 pricerange.

Look at my post above.

There is no way Valve gets away with selling it for that much.
There are other pre-buildt pc's more powerfull than the steam machine in the 800$ price range.

At that point, valve is over charging, or selling only on its brand power.
Its dead in the water if it goes for like 800$.

But the Steam machine is likely to have a controller of some kind. Also, they like money and it's not like consoles wouldn't be really expensive these days, as they'll likely price it competetively to consoles.

Sell it without the controller then. 
I assume most PC users that want to buy a steam machine, already have a keyboard/mouse and a controller of their own.
If they can sell it cheaper that way, they should do that.

Also this is a weaker pc than the base PS5 is.

There already are, consoles out there, competing against the steam machine.
That is the Playstation 5 and Xbox Series X. 

If they want to win over the consoler user, they can't have price of entry be much more expensive than the base consoles.

They like money. but also, what is the number they expect to sell it. The less they sell, the more profit they need to make per console. Steam game sales don't depend if the system sells, so there's no point to sell it any way cheap. It's a custom built system anyway with apparently a custom motherboard and custom GPU (or CGPU).

I am going to guess $650 for the base model. Similar systems from small Chinese manufacturers cost about that and Valve can discount the price close to cost because they intend for this to be a complementary good to their software platform and OS rather than something to make a profit in itself. 

Here is a Minisforum Elitemini HX77G for $659. 

https://store.minisforum.com/products/elitemini-hx99g-hx100g

It has an 8 Core 16 Thread Zen 3+ processor, 32GB of Ram, a 1 TB SSD, and an RX 6600M. 

The Steam Machine has a better and newer GPU, but it will save with the 6 Core 12 Thread CPU (even if Zen 4 rather than Zen 3+), 512GB SSD, and 16 GB of RAM to make up for it.