It's possible to all play together in the same room and keep the instruments isolated,(if the studio has enough sound proof rooms). This way you get the correct feel. We record altogether, in the same room at the same time as the drummer, however the bass amp is in another room, so is the guitar amp. Sometimes I record the bass direct through a sans amp bass driver.The keyboard sets up in the control room & plays direct, the vocalist is in a vocal booth. When recording in studios with no vocal booth, we will have the singer sing "scratch vocals" at a lower volume which we use for reference, and then overdub later. This will minimize any bleed, but we still have the vocals to keep us in place. We all hear each other through headphones.
I've even recorded in a one room studio where the engineer had a home-made isolation box for the guitar to play through. It was a brilliant contraption. He built a soundproof box with a ten inch speaker inside the box & a microphone. The guitar player could blast as loud as he wanted & there was no bleed whatsoever. He just needed to plug his amp head right into the box. I went direct & played in the same room as the drummer. With each instrument on it's own track, you will get a fuller sound and certain items can be brought out more in the mix or brought down. For example, cymbals. Nothing can ruin a song like over-ringing cymbals. If cymbals are not mic'd properly they can create a wash of white noise. If you play altogether, with no separation, you're stuck with it. Another trick, for studios with little isolation, and this takes some practice, is to learn the songs thoroughly so you can play them instrumentally with no vocal track at all. Then the band is all playing together, getting the correct feel, and the only thing needed to overdub, is the vocal track.