While I agree with both answers given so far, I feel they are touching only some aspects and somewhat miss the most important one:
It is actually less expensive to not build a game into the console.
With this fixed, several other abilities come for free:
- Different default games for different markets
- "New" seasonal packages like "Terminator" for Thanksgiving, "ET" for Christmas
- And, as Stephen mentions, easy exchange of the default game if it sucks (*1)
Related to the last but somewhat less "glamorous":
- Exchange of bugfixed versions without opening the console.
And of course, we all know,
- Marketing likes to be able to change a setup until the very last moment.
It seems to me that it would've been cheaper to put the ROM for the game directly onto the console mainboard,
Not really. The cost of a PCB is directly related to its size and number of holes drilled. While integrating them might save a bit of PCB area (not much), it will carry at least the same amount of holes to be drilled.
But more importantly, as Martin mentions, there need to be switching hardware. Even with just a switch, it will be far more expensive than the saved PCB area, not to mention at least two more holes. Anything more considerable than a mechanical switch (*2) will at least need some TTL and/or some I/O pin to control it. While the first adds lots of through-holes, I/O is as well a rare resource on these early systems.
In any case, mounting a default game in a simple console like the VCS will always increase cost, as the relevant factors do not scale by volume. Such consoles already start at a production volume that maxes out the usual volume related savings, so every square centimetre and every hole will add linearly.
This of course changes as soon as it's about a console that already includes a boot ROM. A great example here is the Vectrex which came with Asteroids preinstalled. The console had a preinstalled OS ROM, so adding a game was rather a case of more ROM/filling up the ROM. Having a Full 64 KiB Address range it was "simple" to put the built-in game at a different address and use OS software to detect the presence of an external game or not. Here it really comes down to just another socket.
and let it be the default program the machine runs on boot when no other game is present,
Which does mean a way to detect and switch, adding to the cost of the base device by either hardware, or some OS plus hardware.
thereby saving the cost of a circuit board and cartridge case.
But at the cost of an increased base PCB, increased by more than the cartridge PCB would be, making it more expensive. Not to mention that basic game PCBs had to be manufactured anyway. Similarly for cases: they are needed anyway and production cost is negligible once the forms are made.
In addition, putting the game directly on the mainboard would halve the number of cartridges needing to be plugged in and out when switching between that and other games.
Beside that this is a very long term consideration, and it depends on how often one will use the base game - which is an argument that can be made for any game cartridge, as the first one is no different. Also, how often will people have played Combat after they got more sophisticated games?
Is there a reason I'm missing, why pack-in games were provided as actual cartridges rather than ROM chips on the mainboard?
It's cost and flexibility, but mainly cost.
Browsing thru Curt Vendel's faboulous book Atari, Inc: Business is fun, to understand a different question, I stumbled about a related direct quote:
"Shortly after the design was conceived, we went to an external ROM connector instead of the ROM being on board. Other concept ideas were to use a stack of ROM chips and be able to select a game, like a jukebox" recalls Steve Mayer
Steve Mayer was part of Cyan Engineering, a division of Atari, responsible for the development of many of Atari's hardware, including the VCS. The quote is reffered for as 1975 during the very first stage of VCS development.
So while it's not surprising that various concepts were considered, it's nice to find a hint about.
*1 - Just think what a huge success the ET-package would have been. Having the game not on board makes refurbishing the unsold boxes to some other special edition a simple task of replacing the game cartridge (pack) and slapping a new banderole before shrink-wrapping again.
*2 - A switch will of course add mechanical issues when being operated every single game change.