- Browning after cooking through works better because the surface is already dry;
- Its to speed the cooking.
Both of your questions are all about the water, so it is important to understand how water influences the way that meat cooks.
Water, as is well known, boils (at sea level, anyway) at about 100 C / 212 F. What is not well known is that the amount of energy to take liquid water at just at 100 C to steam just at 100 C is comparatively very large. This energy (required to break the inter-molecular hydrogen bonds as water is a polar molecule) is called the enthalpy of vaporization.
In order for a water molecule to jump from the liquid at the surface of the food, into the free steam above its surface, it must absorb enough heat to "pay for" the ehnalpy of vaporization.
This means that when water evaporates, it actually cools the surface (which is why sweating works for people). Conversely, when steam condenses on the surface of the food, it warms the surface because the enthalpy of vaporization is metaphorically paid back.
This process ensures that as long as their is liquid water at the surface of the meat (including being replaced from the interior as fast as it evaporates), the surface temperature of the meat cannot exceed 212 F / 100 C.
In order for steak or any other meat to brown, it must be brought to temperatures on the range of 250 - 300 F, at least, for the Maillard browning reactions to happen at a reasonable pace. This cannot happen when there is free water left on the meat because the temperature will be too low.
So the best way to brown meat is after cooking it through at low temperature. The low temperature cooking will have dried the surface, and it will be relatively easy to brown the surface for good flavor. This will also lead to less over cooking at the surface.
A roast in the oven that is uncovered cannot obtain a surface temperature higher than 212 F so long as moisture from the interior flows to the surface and keeps it wet. The evaporative cooling will ensure this. This means that the heat conducting into the center is also limited to 212 F, and it may take a while to bring your roast to its desired temperature.
By wrapping the roast in foil, the steam evaporating from the surface is trapped close to the roast. Eventually, the vapor pressure inside the foil will be such that water condenses back onto the roast almost as fast as it evaporates, essentially shutting down the evaporative cooling, as condensing water returns the energy lost in the enthalpy of evaporation.
So the surface temperature of the meat can now climb above 212 F, and thus allow conduction of heat into the center of the roast more quickly, allowing it to cook through to the desired temperature more quickly.
Of course, this is at the cost of keeping the surface moist, so won't develop crust as well. This is why the foil is usually removed towards the end, so that the surface (which is quite hot) can now dry, and allow the delicious browning to proceed.