Why is the collector region doped?
The essence of transistor behavior in the active region is as follows.

The base-collector pn junction is reverse biased
majority carriers have a difficult time crossing a reverse biased pn junction
minority carriers easily cross a reverse biased pn junction
unless the emitter injects minority carriers into the base, there are few minority carriers in the base
when the base-emitter pn junction is forward biased, majority carriers from the emitter cross the base-emitter junction into the base, where they become minority carriers, (where they easily cross over the reverse biased base-collector junction).

Now:

As long as within the active region the collector-emitter junction is reverse biased, is there a purpose for which the collector must be doped?

The conductivity of the collector depends upon doping. Undoped silicon is a poor conductor.

Moreover, not only that it is doped, but it is moderately doped, thus more than slightly doped like the base region.

The base is lightly doped to reduce the number of majority carriers in the base. The concentration of majority carriers is directly related to the doping concentration. The higher the concentration of majority carriers, the greater the chance of the minority carriers recombine in the base with majority carriers. This increases base current, and decreases collector current.
The collector is doped less than the emitter to make the transistor asymmetric. The more symmetrical a transistor, the poorer it performs in the forward active region (but the better it performs in the reverse active region).
Those are the reasons why the base and collector are both doped less strongly than the emitter. Why the base might be doped even less than the collector I do not currently know. Perhaps someone with more expertise in transistor design can answer.