You Need a Plan, Just Not a "Business Plan"
A common mistake small businesses make is thinking they need to operate the same way as massively scaled enterprises with thousands of people on the payroll.
"If the big, fancy, successful companies are doing it, then it must work!"
But, your biggest advantage as a startup is that you're able to make local decisions and change course quickly! In fact, it's common for a well-functioning team to dig into a customer problem in the morning, brainstorm a solution, and ship an improvement that same afternoon.
Mature companies with years or decades of bolted on processes and code debt can't match that sort of responsiveness!
And so, in the same way that you should ignore the engineering practices of large companies and embrace your small, nimble nature; ignore the business planning practices of the big guys and adopt an equally nimble approach to planning.
An approach that many startups have used is the Business Model Canvas developed by Steve Blank, and adapted by Ash Maura as the Lean Canvas.
Each of these tools have their pros and cons, and neither are perfect. But one thing they have in common is that whatever you write in them on Day One is very unlikely to be what is written down on Day One-hundred and One.
The temporary nature of the Business Model Canvas is a feature, not a bug.
Your plan should be able to adapt to what you learn from your customers as you build, test, observe, repeat. If you spend weeks or months working on and revising a forty-page "Business Plan" in the early days, you'll be subconciously invested in proving it right to convince yourself all that time wasn't a waste.
With a Business Model Canvas, you can hammer out Version 0.1 in an afternoon at your favorite coffee shop and look forward to revising and improving it upon first contact with your customers.
If a conventional Business Plan holds any value for a typical startup, it's that it forces the founders to think through the many challenges they're likely to face. That's a good thing, but instead of investing a boat-load of time on bizspeak prose in a Business Plan, jot a couple bullet points down on your Canvas and spend the rest of that time testing your hypothesis in the real world.