Integer BASIC was part of the original ROM. If I had to make a guess, it defaulted to the monitor since you could buy machines in a 4 kB configuration. Even though Integer BASIC was in ROM, some memory would be used by the interpreter and some memory was used for video. That wouldn't leave much memory for software. (Heck, 4 kB wasn't sufficient to support high-resolution graphics.)
Loading Integer BASIC from cassette was a thing, but that was after the autostart ROM was introduced since AppleSoft and Integer BASIC were not compatible.
Loading Integer BASIC from cassette was a thing, but that was after the autostart ROM was introduced since AppleSoft and Integer BASIC were not compatible.