Don't remember the Atari ST to be cheaper (at least the 1040 which was comparable to the Amiga 500). The cheaper ST models had no disk drive and required the purchase of an external drive. You were also limited with the monitors versus the TV set that was supported by the Amiga. Maybe I should look for some old magazines since memory might be failing me...
And I honestly don't remember Atari ST software bundles but I was never really interested in the ST so I must have just missed those...
And even in the early days, Commodore was licensing Microsoft BASIC as part of the operating system in earlier 6502 based machines. At that particular time Microsoft BASIC was the defacto standard.
If they released the Amiga without a BASIC interpreter, they might alienate the C64 users converting to the Amiga. It also served as an educational tool for the novice user. If you spent a lot of money on a computer, you at least want to be able to "play around" a little without having to buy something else.
You say AmigaBASIC is buggy because some programs didn't run correctly but that doesn't mean the interpreter was at fault. Commercial games did not use AmigaBASIC since they most certainly were compiled using Absoft's compiler. Was not aware that Absoft itself also created a BASIC interpreter since as far as I knew, the compiler was intended to compile AmigaBASIC programs.
Never heard of True BASIC, not even on the PC. Must have been one of those obscure languages like Modula-2 or Draco.