Even if business plans may seem obsolete, its a nice way to get your thoughts and plans sorted, written down in a well reading way. It probably helps you as the founder the most and might also give you new ideas because you suddenly analyze so many competetiors and the market in a deep way. I have written a business plan and while probably nobody read it (just guessing), its still always a good thing to be able to send someone a well thought out 30 page plan when requested. (we got funded)

Its not that much about the businessplan itself as about the fact "ah ok, so these guys have actually thought this through and are serious about it"

Of course you should still have a good 10-15 slide presentation about the most important stuff, because people will actually look at that ;)