"Are new Friars expected to petition to join an order?"
"expected?" No, I don't think so.

"...encouraged to consider?"
Well, yes, but that consideration should begin with an careful assessment of ones skills, available time, etc - - after which, if the Brother indeed concludes that s/he should petition to "join an order," I believe the gods will consider the needs of the Monastery; the adequacy of the Monks skills; and the promise the Monk has shown by prior deeds (nodes, considerations, attitude, among others).

(re the 3 questions in your last para)
It depends! (but re the last, see above.
"be most useful?" That may be best decided by you.

And, some random NON-authoritative thoughts:

• re janitors: Theirs is a responsibility that demands a very broad and deep understanding and appreciation of the standards (and local mores) which guide them (See How do I use the power of consideration responsibly? for an introduction) ... and, since so much of the janitors work deals with markup, the preferred markup here.
• re the inactivity level of most pmdev's and re "Is the codebase really that scary?
  yep! and (IMO) yep, unless you have a very high skill level and a large amount of time to familiarize yourself with its structure.
• "largely rejected by the gods?"
  I don't think that many pmdev offerings are so much "rejected" as "non-existant" or "found wanting; tabled for further refinement."
• "The allure (is) by virtue of the orders being, well, exclusive." That's probably not a really good reason for committing to an order... nor a reason that will find favor with the Appointing Powers unless the applicant brings more than ego to the table.

Thank you for an interesting and insightful question.
I think ww gave an excellent answer, but I'd like to add a few observations.

First, it's not really "fair" to compare the sizes of the various orders, because they are so very different in many ways. What they do is different, and they have wildly different histories, including particularly their rates of induction and dismissal of members. They also have very different levels of appeal to the general population.

I think it's safe to say that pmdev has been very popular, in part because membership in pmdev allows people to peak behind the curtain of PerlMonks' workings. I dare say many of the people who have joined pmdev did so solely to view code, not to contribute changes. The various orders have different levels of power, so the gods induct new members into them with different degrees of solicitation and vetting. Janitors have a lot of power, and so are held to very high standards of conduct; abuse of this power can (and has) resulted in summary, permanent dismissal. Similarly for Power Users. But only a handful of Power Users are needed, because of what they do; and having too many can actually lead to conflicts. In contrast, a pretty good battalion of Janitors only serves to make their job easier.

Other orders — SiteDocClan, pollsters, Pedagogues, etc. — aren't quite so restrictive; primary qualifications are a burning desire and a modicum of trustworthiness and PM experience.... but they just don't have as much broad appeal. That said, not all applicants are accepted. This can be due mainly to a lack of workload. The workload of SiteDocClan, Pedagogues, and QandAEditors currently is quite low — easily enough for one or two dedicated persons to handle. This has been different in the past, and, @Larry willing, will be different again in the future. :-)

See Cabal Matrix to get a real idea of how active the members of the various orders are.

(Note that this discussion does not cover the fraternal orders, which have no official role or power in PerlMonks.)