"Why do I need a local church? Is the value of fellowship with God and saints that critical?"

Apart from the many great answers given, I'd like to add something.

I've noticed these questions come from a misconception about our faith.

Demons also believe and tremble.

What Christians have with God is more than just an acknowledgement of the existence of God.

There's a love component to it.

We don't just believe in Jesus. His sacrifice for us made us love Him.

We love Him because He loved us first.

It's faith working through love.

The question of the necessity of fellowship with God and saints come from this subconscious idea that being saved is just about believing Jesus died for you.

No one believes Jesus died for Him and doesn't love Jesus in return.

There's no saved man who doesn't love Jesus.

So how can you claim to be saved and feel no necessity to hang out with the lover of your soul?

How does a saint feel no urgency to have a romance with their Father and their siblings?

If someone saves you, you should want to know them.

The contrary is an aberration.