I never got an answer to my question so I thought I'd bring it up again!
From an outsider's glance, it seems there are a variety of benefits from joining the Roman Army as a member of the equestrian class, with opportunities for battle, prestige, and even a chance for political power or in the imperial period, the Emperorship!
Meanwhile, the navy seemed relegated to a second-class service where you'd be commanding mostly non-Romans, primarily fighting pirates (I'm guessing less loot there versus sacking a Persian city), and there doesn't really seem to be a Navy->Emperorship pipeline
So, if I am an ambitious young eques, why would I consider a career in the Navy over the Army? Would certain families or regions groom their young men for the navy? Were the benefits more considerable than it seems?
Much appreciated in advance!
You're absolutely correct that, most of the time, the Roman navy was the red-headed stepchild of the Legions. Where I think your premise may be wrong is that you may be picturing something like the modern system of recruitment, where an officer might be able to walk into the army recruiting office, or cross the street and walk into the navy recruiting office instead.
This does not accurately capture the way the Romans staffed their fleet command for most of their history. Roman navies were, or could be, commanded by magistrates or promagistrates, but the permanent officer corps was, in various proportions and at various times, composed of foreigners or freedmen who were not eligible for commands on land, of civilian administrative officials and port authorities, or of army officers who were assigned naval posts during periods when the administrative delineation between army and navy was not particularly clear.
Sextus Pompey is said to have used two of his father's freedmen as admirals (his noble adherents fussed at him about this), and we get specific descriptions from the Battle of Actium of the exploits of a Cilician admiral on Antony's side and a Spartan one on Octavian's. Nero is said to have attempted to murder his mother using the navy, an idea that was suggested by a freedman who was "prefect of the fleet at Misenum."
The idea of an ambitious young member of the equestrian class deciding make a career in the navy is not impossible, but would have been extremely unusual for precisely all the reasons you raise in the OP. In general, career naval officers in Rome were not high-class, and in many cases were not even Romans. During the Republic, you'd only get high-class Romans commanding fleets in battle during major wars, and even then, they were forced to make use of officers from other classes or other nations. It's a bit off topic for your question, but it is also the case that even the ships and crews themselves were bought, rented, or borrowed from foreign navies to meet immediate emergencies- it was on a diplomatic mission to accomplish this that the young Gaius Julius Caesar was alleged to have bought a fleet by performing sexual favors for king Nicomedes of Bithynia.
Efforts were made during the principate to standardize the system, and during the Flavian period a formal requirement was added that the post of prefect of a standing fleet could only be granted to someone who had gone through the militia equestris. However, foreigners and freedmen continued to hold posts of considerable authority in the Roman Navy at least into the third century.
ETA source: D.B. Saddington (2011) [2007]. "the Evolution of the Roman Imperial Fleets," in Paul Erdkamp (ed), A Companion to the Roman Army, 201–217. Malden, Oxford, Chichester: Wiley-Blackwell. ISBN 978-1-4051-2153-8.
Followup: I was under the impression that the Roman Navy was primarily an auxiliary/mercenary force for precisely the reasons OP outlined. Did the Romans generally recruit foreigners for their navy, or would Roman citizens also join?