You’re not overthinking it at all and have hit upon an important point. The problem with “ten” is that it’s too easily confused with 1010_2 or 0x0A_16. One-zero base 2 is unambiguous. Also one, ten, eleven etc would get very unwieldy very quickly, and as it already gets unwieldy very quickly even when just quoting digits, that’s why we have hex and octal.
You’re not overthinking it at all and have hit upon an important point. The problem with “ten” is that it’s too easily confused with 1010_2 or 0x0A_16. One-zero base 2 is unambiguous. Also one, ten, eleven etc would get very unwieldy very quickly, and as it already gets unwieldy very quickly even when just quoting digits, that’s why we have hex and octal.