The exact doubling period changes whenever the government revises the applicable interest rate — it has generally hovered in the range of roughly 9 to 10 years in recent notifications, though it's worth checking the currently notified rate and period before investing, since this isn't a fixed constant across all time.
KVP is available in relatively small minimum denominations, making it accessible, and it doesn't have the same tax-saving benefit that PPF or ELSS offer under Section 80C — this is a savings and capital-doubling instrument, not a tax-planning one. The interest earned is also fully taxable at your income slab rate, unlike PPF's tax-free interest.
It tends to appeal to conservative savers who want a straightforward, government-backed way to grow a lump sum with no market risk and a clear, easy-to-understand doubling promise, rather than investors optimising for either tax efficiency or maximum returns — for those goals, other government schemes or market-linked options are usually more efficient.