I think if you booted in this mode, BASIC had no access to the floppy drive at all so you couldn't save your work (or we kids didn't know how). Better to boot from a floppy, then after it finished booting, swap the floppy for another one to save the silly BASIC games we were writing.
Later on, we saw models with two floppy drives, so you could leave the floppy containing DOS and BASIC in drive A: and save your work onto the disk in drive B: Eventually, PCs began to come with hard drives and these naturally became drive C: So if you've ever wondered why Windows typically refers to the hard drive containing the OS as drive C: it's because drives A: and B: were the floppy drives.
That's true. The PCs had a BASIC in ROM and a cassette port. That was dropped starting with the XT, which gave the puzzling "NO ROM BASIC" message in 80-column text when the hard disk was not bootable.
When you booted a ZX-80, 81, Spectrum, a VIC-20, a PET, or an Apple II+, you went straight into a BASIC interpreter (or REPL, for the initiated). You could enter a program, or issue commands at will. We rarely think about this, but the first UI you see in those machines is a programming language.
And we did program a lot with those machines.
With a CP/M machine or a DOS PC (there were about 2 people in the world with PCs without floppies ;-) ), you boot into an OS. It's not a programming environment, but one designed for starting applications someone else wrote. While most had a BASIC interpreter you could run, it was a standalone program and not THE language of the machine. And experimenting COULD harm the computer - you could delete files from your DOS boot disk, as many of us discovered the hard way.