No it is not. And to find out why, please keep clicking. Basic reason is more space, privacy and independence. The correct comparison is probably a studio apartment (which are rare in Jakarta, although we’ve actually got one here).
You’ll find here a 2010 list of kosts (with pictures and prices). None of areas considered high risk by the Australian Embassy are are included on the list. The list is currently being provided to students in Australia by a consortium of Oz unis with plenty of on-the-ground here. Just for you.
So, I’m told kost it comes from Indekost (upper case?) which means something like “a place to stay” in Dutch. It’s shortened to kost in Indonesia (but the “t” is dropped for all practical intents and purposes).
For the most part tourists visiting stay in “hotels” while expats/long-stayers eventually go for an apartment (apartemen) or house (rumah). There are other options, however, with the kost perhaps foremost. Indonesians stay in kosts (which might once have been considered the Indonesian version of an apartment, except that Indonesians are keen on the cement-blocks-in-a-pile type of apartment) for all kinds of reasons: living temporarily in a new city (perhaps as a student), because mom and dad’s house is too small for all their kids, because you can pay month-to-month, because they need the laundry service because they work full time and have more money than time.
The main reason the kost option isn’t better know to foreigners is probably poor marketing. The first step — I would assume — in trying to attract foreigners would be to re-christen the puppy a bed-and-breakfast, guesthouse, hostel etc. Certainly there are plenty of nice kosts. What to ask for? En-suite bath and kitchen, all the normal stuff, including pool (seriously).