How does water behave in Dutch oven baking?
I think we need to deal with the two different elements of the question: first, I'll discuss better oven spring, and then I'll get to good crust formation.
Most oven spring comes from inside the bread.  Air is already trapped inside the bubbles in the dough which expands as the internal temperature rises.  Additional steam is released internally as the dough heats, adding to the pressure for expansion created inside the dough.  The only thing necessary for good oven spring in most breads is allowing these internal gases to expand and evolve.
The main thing external steam does to impact oven spring is prevent early crust formation (as alluded to in the first point in the question).  The mechanism is not only due to cooling, but due to humidity of the surrounding air.  For a crust to form, the dough has to be heated above boiling temperatures.  In order for the dough to get that hot, it needs to lose significant moisture (at least on the surface), effectively drying out.  If a section of dough has substantial moisture, it will continue to boil out.  With normal air pressure, water boils out around 212F/100C, which means that while water is boiling out of moist dough, the temperature of that portion of the dough will maintain a temperature around that boiling point.
By surrounding the dough with high moisture air, you slow the rate at which water boils out of the surface of the dough.  (Water will boil out faster in a low-humidity environment compared to a high-humidity one.)  So, filling your oven with steam will slow crust formation by keeping the outer layer of dough hydrated longer, which means it stays soft and doesn't harden (which would halt oven spring).
The same effect is still possible in a dutch oven, because there's a much smaller volume of air to fill with steam.  A significant amount of moisture escapes bread dough while baking, and there's enough in the early phases to create a fairly moist environment inside the dutch oven, effectively simulating an oven filled with steam already.  As long as a relatively high humidity environment is maintained around the dough, it will delay crust formation and aid oven spring.
The radiant heat from the dutch oven on all sides also may add to the oven spring by introducing more energy quickly into the dough.  (That happens even without the condensation mechanism discussed in the question.  I mean, some moisture may condense back on the cooler dough, though nowhere near as much as with an oven filled with external steam.  My guess is that the condensation mechanism to deliver heat is less important for oven spring than keeping the outer layer of the dough soft and hydrated.  Also, even without significant condensation, moist air will transfer heat faster than dry air.)
The previous paragraphs discuss where better oven spring comes from.  The good crust formation then is also aided by the third and fourth points in the question (extended enzyme activity, which aids in ultimate browning, and starch gelation), both of which just come from the high humidity environment.  In that sense, the &quot;water layer&quot; described in the question still can happen by simply being in a sealed container that keeps humidity relatively high.
It should be noted that most recipes for dutch oven baking state that the lid should be removed for the last portion of baking.  This removes the moisture (as when a steam oven is vented during bread baking), which allows better and more consistent crust coloration as the Maillard reactions can proceed faster in a low humidity environment.  Crust will still form with the lid on, but it may become somewhat thicker before it browns as much as is desired.  (A lot of this depends on temperature, time of bake, hydration level, etc.)  In my own experience, keeping the lid on too long can delay escape of internal moisture from the dough as well, which can sometimes give the crumb a more &quot;gummy&quot; texture even when fully baked.

By the way, do we really need to bake at that high temperature? What
would happen if we could bake at 100º C (212º F) to get the oven
spring and only after work on the crust color?

No, you do NOT have to bake at a super high temperature.  In fact, some people bake successful loaves of bread starting with a cold dutch oven.  See, for example, this blog post from King Arthur flour for some tips.  They ultimately concluded that one should use an enclosed container with a smaller base if starting from a cold temperature.  Although they don't explain why, my guess is that the long time it takes for the temperature to rise allowed a bit too much gas to escape before the bread solidified internally, leading to a slight collapse and a final loaf volume that was a bit smaller.
That said, I'd say that effect is somewhat recipe and dough dependent, as well as dependent on how long it takes for the dutch oven to heat up.  It's certainly possible that in some situations a bake started with a cold dutch oven could give an equal or even superior oven spring to a loaf started in a hot oven.  You're balancing two things: (1) crust formation can't happen too quickly, or the oven spring halts before the rise is complete, but (2) structure needs to set quick enough before gases migrate out of the dough, and the gluten isn't sufficient to continue to hold up the expanded dough (without the set internal structure).  Starting in with a cold dutch oven avoids the first, but could cause problems with the second.  If the timing is right, though, one could maximize oven spring and still get good crust formation and color at the end.  However, at some point, one does need to finish with a rather hot oven to get the browning and &quot;crackling&quot; element of the outermost layer of crust in a lean dough.