The church is called the body of Christ, and individual Christians are like parts of a body (1 Corinthians 12; Ephesians 4). Different parts have different purposes and gifts. Each body part needs all the other body parts in order to function well. The health and functionality of an individual body part depends on (1) whether or not its connected to the body and (2) the health of the other parts.
I suppose you can still be a Christian and not be faithful to one local church. But you most certainly cannot be as healthy as you could be, nor can you function the way God intends.
Here’s an attempt at a practical application:
The Holy Spirit gives gifts to people so the body can be built up (1 Cor 12). If you’re a Christian, He’s gifted you in some kind of way–teaching, mercy, hospitality, discernment, whatever. This fact necessarily assumes you’re going to be around other Christians on a consistent basis (the same Christians) in order to actually use the gift.
How can you use your gift if you’re not around the same Christians on a consistent basis? It takes time to build relationships of trust in order to let someone come into your life and be comfortable with them. If you’re constantly changing churches, don’t go to church at all, or don’t go enough to build any kind of legitimate relationships, how can you use the gift the Spirit has given you? You can’t. At least not well. The result? You suffer from not benefiting from the gifts of others and the body suffers by not benefiting from your gift.
Not to mention other benefits of being committed to one group of people: accountability, purpose, friendship.
Being uncommitted to a local church doesn’t mean you’re not saved. But it does mean you’re not healthy or functioning the way you could be–like an organ on ice.