In my honest opinion, a partially planned thing helps you course-correct for survival or growth faster rather than a perfect planned thing where you spent so much time on so many things, and in the end you find out that this whole thing didn't work as planned.
In my experience, start up with a partial plan and make it perfect along the process.
But yes, you need a plan in whatever level of detail is appropriate. For some projects you just need a general direction to go in (say "Figure how the colors got screwed up in this print and how not to have it happen again" -- that kind of research project is super hard to estmate), but if you were building a building and expecting to get permits, funding from a bank, rent a big-ass crane, you will need a very detailed plan.
Even if you have a detailed plan there is a lot of expectation that something could go wrong.
A task lisk and
https://en.wikipedia.org/wiki/Kanban
is the minimal project management system for small projects.
https://www.pmi.org/standards/pmbok
describes just about everything you need to handle for the most complex projects, smaller projects need some subset of those practices depending on the project.
Then it wasn't a perfect plan, because it would have worked out perfectly, right?
This is one of the big sticking point between BDUF and non-BDUF approaches. Spending inordinate amounts of time creating a plan that won't survive is not valuable, it's wasteful. Spend enough time to create enough of a plan, then execute and refine. How much is enough? Hire me and I'll tell you. More seriously, gain experience in executing and you'll figure out when it's time to just start and stop sitting on your ass in meetings all day. The context of your effort, your team's level of experience with the domain, and a few other factors are what help to determine the switchover point from planning to executing.
Your perfect plans are drawn around a set of hypotheses and premises, chained unfortunately, some of which I'm not uncertain would be proven wrong the moment you'd try and execute.
I am reminded of this: https://www.youtube.com/watch?v=uDJEjT2kKqY . Trey Parker and Matt Stone, of South Park, on story structure. This is what mostly happens.
I'm also reminded of that scene from the Collateral movie, where the Jamie Foxx character talks about his business plan, the one he's been refining for ten years.
Don't sell the pelt before shooting the bear.
Think about Donald Rumsfeld's advice: your first plan should contain all of the known knowns, good estimates for known unknowns, and wiggle room for the unknown unknowns.
And keep it as complete as possible. If your board, or your investors ask you where things stand, you must be able to give them as complete of an answer as is humanly possible.