I know many people who didn't. Even myself, after ~1900 I didn't have a coach, only friends and acquaintances whom i could ask something.

I don't say that one doesn't need a coach to become div1, but having a coach absolutely is not a necessary condition to reach some certain level (at least up to read)

Neither I deny that with a good coach you will in fact most likely reach it sooner. However, if one is stuck at some point, I believe just something is wrong about his approach/attitude for trainings, and that's the first thing that has to be changed before getting a coach

It is certainly possible, I am not a CM but until very recently I had no coach and no friends that did CP. Everything I did, I did it 100% by myself.

I did get everywhere I am without having had any formal coaching besides having been introduced to C++ and the very basic algorithms, however I would have done it much faster if I had a coach or someone to mentor me throughout the process.

However, online communities such as Errichto's server are very useful and I've seen a lot of people improve over time as they learn from more experienced peers. Even back in the day when I used to be a more active competitor, being an active member in various discord servers was very helpful especially as far as making the step to more superior echelons of competitive programming, so yes, getting to purple is possible by yourself, however having someone to guide you can be very useful.

I can solve < 2200 pretty easily and I don't have a coach.

Master here. Trained all by myself since March this year with no coach but a few friends to discuss with.