This was more of a marketing question than a technical one. The historical fact is that most vendors of 8-bit personal computers chose to include BASIC. The simple answer as to why they made this choice is pretty obvious - It was the standard.
So, slightly restating the question posed, one could ask "Why was BASIC the standard?" It was a standard in the sense that all the successful early entries to the marketplace included it. So, if a vendor wanted to compete in this market, they needed to offer feature parity with the competition first, then try to build from there. And the inclusion of BASIC was widely regarded by consumers as part of the feature set from the earliest personal computer products (Note 1).
- Altair 8800 (1974): Microsoft BASIC available as an add-on.
- Apple ][ (1977): Built-in BASIC, followed quickly by an enhanced version also from Microsoft.
- Commodore Pet (1977): Built-in Microsoft BASIC
- Tandy TRS-80 (1977): Built-in Microsoft BASIC
It's pretty easy to see a trend. Not only was inclusion of a BASIC dialect rapidly becoming standardized, but a familiar vendor was already dominating the market for licensed 3rd party BASICs. Indeed, Microsoft "cut its teeth" by dominating the market for BASIC more than a decade before the emergence of the "Wintel" standard. And MS-DOS was no slouch in terms of being a de facto standard OS in the interim, as well.
Note 1: The question appears to be about 8-bit personal computers, not earlier mini-computers or other devices that may have contained a microprocessor and which support a BASIC dialect.