It is just two completely different mechanics though. The Arkham arrest is merely a delaying tactic. You lose the rest of this turn (no encounter because there is no Jail specific encounters) and then move to the police station But you lose the rest of this next turn as well so you skip the encounter again. Then you are free to move on the 3rd turn (or stay and have an actual police station encounter). It is just a nuisance.
Innsmouth is actually a dangerous place. You get thrown in there and you have a chance to immediately get devoured. You have a better chance of escape, of course, but it is highly up to luck at that point since you typically won't have adjusted your speed to give you more cards to draw. And even if you are lucky enough to escape on the very turn you get thrown in, you are still delayed, meaning you have to spend one turn on Sawbone Alley. If Martial Law has been declared, there is a good chance you get thrown right back in.
I am not a huge proponent of the rule of thumb that you "do what hurts the investigators most" but I do think that is the driving principal here. It is more harmful to an investigator to lose a turn in Arkham. It is more harmful to an investigator NOT to lose a turn in Innsmouth. And this follow the thematic slant of Innsmouth perfectly, I think.
If you skipped an encounter and lost the next turn, that is two chances to revise your Sneak during Phase 1. It is also a lot more time to get other investigators in Sawbone Alley to increase your chances.
Finally, if you applied the Arkham rules exactly as written, the sequence is actually you would have an encounter the turn you are thrown in jail (remember, it only says lose next turn - you are assumed to lose this turn because there is no means to have an encounter anyway). Then next turn you skip an encounter. Finally, you would go back to having an encounter. That makes no sense but is RAW.
So I don't think the omission is an oversight at all. I believe it is written as intended and the jail mechanic is completely different. The reference to Arkham Jail is to be clear it doesn't apply and then they go on and explain how you deal with Innsmouth Jail: delay, lose 1/2 money. That's it. The cards take care of the rest.