Why do shrimp / lobster / crab turn pink or red when cooking

My guess - and this is just a (somewhat educated) guess - is that it's just to promote more even cooking.

Since you're talking about a layered dish, some parts are definitely going to cook faster than others. If the entire dish starts from room temperature, as opposed to fridge temperature, then that means less time is required to cook it through. Less time and less heat required to cook means that all of the layers will be more likely to end up at similar internal temperatures - as opposed to having burned bread, liquefied cheese, or rubbery eggs (I'm not sure offhand which cooks the fastest).

Even if it's not an issue with the thermal capacities of your individual ingredients, you're also layering these each several times over, creating a very dense product, so there would still be a significant risk of the middle layers being undercooked, or the outer layers being overcooked.

You might be able to bake it straight out of the fridge; however, you would definitely have to increase the cooking time to account for the temperature difference, and there are a lot of variables that come into play which would affect how evenly it cooks: the intensity and location of your oven's heat source(s), the density of the casserole, the kind of baking dish you use - I probably wouldn't chance it, at least not when preparing this for other people.

You tend to see the same recommendation for anything particularly dense, such as a roast, or anything layered, such as a lasagna, and generally, you do want to follow those recommendations for the same reason. They cook rather poorly if you cook them from cold or frozen, leaving you with a charred surface and an only-mostly-cooked interior. It can still happen even if you start off at room temperature, but it's less likely and the effect tends to be less pronounced.

Viscosity of the cold dough is probably too high for good rolling. It's tearing and blobbing rather than feeding smoothly through the rollers.

I'm not finding a ref for rolling, but for extrusion:

The ideal temperature for pasta extrusion is between 45 and 50°C, as anything above 50°C will denature the proteins, impeding gluten production and therefore resulting in a soft sticky product. Using a cold water jacket will cool the dough and barrel too much, resulting in undesirable dough viscosity.

Nice plot of dough viscosity vs temperatures here (fig. 4.3), but it only goes down to 30°C (86°F) Lower temperatures, including heating within the extrusion die, are likely not usually encountered.

This pasta rolling cook states:

In making pasta it is important to avoid cold so use room temperature eggs. Also, do not work on a naturally cold surface such as marble or stainless steel.