Does it make sense to open the Bilt card with a $5k mortgage if I already have the CSR?

I have a $5,000/month mortgage and I'm trying to figure out if it's actually worth opening the new no-fee Bilt card.

The catch: I already have the Chase Sapphire Reserve, which I use for all my dining, DoorDash, and travel. I also use store cards for Amazon and gas.

To hit the new Bilt spending hurdles and get a decent point multiplier on my $5k mortgage, I would be forced to put my groceries, utilities on the Bilt card just to reach the $2,500 or $3,750 monthly minimums.

My main question: Does it make sense to open the Bilt card in this scenario, or is the juice not worth the squeeze since my heavy spending goes on the CSR?