Yes, granted, but there's not an unlimited number of planets out there either.

Have you heard the puzzle about the bacteria colony that doubles its area in the agar tray every night? On day 10, it occupies half the area. How long before it occupies the whole tray? One more day. You can add another agar tray or ten or a thousand, but it doesn't buy you that much time.

At a constant growth rate, if the solution eventually involves spreading to multiple planets, it's just a few more centuries before we're running low on planets, almost regardless of the size of the galaxy.

It’s unlimited on any practical timescale an individual should reasonably care about.

We could all be dead, or society be reduced to medieval levels where the technology to leave our gravity well no longer exists.

Not even sure if that's about space or about heaven. Same baseless belief in salvation to me.

We aren't going to be shipping billions of people off to Mars. We'll send some small number and they'll reproduce over there. Having a backup will be great, but it does nothing to address the population that's already here.