This is basically what Bloomberg has done. Despite selling financial terminals to bank traders, the company still hasn't gone public after all these years.
I think it is no-brainer that founders would prefer to have full control and ownership. If you manage to bootstrap a profitable company with zero outside funding, great for you, but that's not the typical case. Most of us need some money to make money.
Good ideas are easy. Unique good ideas are so rare as to be non-existent. Nearly all good ideas are obvious to anyone who knows the field and what can be done.
You can have other companies eat your lunch. All you need is to get into a default alive state. I.e. have 5-10K MRR. The rest is nice to have. It should be possible in any billion dollar market.