Even as an Independent, the people who you are doing missions for will keep track of how they feel about you (your Rep with them). Failing a mission will make the ones you took it from less happy and completing them more, which is a good thing to keep track of as better rep means better (paying) missions. For each minor faction you gain rep with, if they are affiliated with one of the supoerpowers, then you get rep with those too. Right now that makes no reall difference in game-play, unless you push to get yourself hated, at which point you'll find lots of system authority ships on your tail, or climb the ranks to get access to certain system / ships.
Most of the time, if you're just going from system to system without settling down, you'll stay fairly neutral with everyone and never need to worry, but once you find yourself a 'home' system, the way your actions affect the BGS, and thus how the local factions see you, will become a fun extra level to the game
I've got a brother in law, that's been an indepent owner operator his whole life. Though his style of going where ever the good load needs to go, he doesn't get home much. His wife aquaits it with being married to a soldier; Except WAY more money. The process for choosing loads is the same in his rhelm, I'm always have at least one load going somewhere when I check the board. If there another load going somewhere in route over 50,000 it's mine. I have a t6 and it can really haul some freight when it needs to. So, yeah, I'll be an indepentent for ever. If and when I ever find a Doplhin, I'll continue playing the same way, going where ever the money is.
My brother in law states, if the wheels aren't moving, your not making money, and moss doesn't gather on a rolling stone (to all you millennials, I don't mean the band). LOL