Less expensive 1 3rd less board footage of lumber fewer pieces to handle fewer joist hangers to have to attach and only one half as many screws to attach the roof steel.
Ok to use 2 x 4 for for roof rafters.
The secret word is truss.
The back of the roof will attach to house with 16 2x4 and lag screws.
Front and sides will sit on deck on a 2x4 wall with studs 24 oc and screened in.
Rafters to 2x4 with joist hangers.
At the pitch range you are looking at the 2x4 is just fine up to 8 6 depending on the lumber grade.
Also if you want to make things cheaper you can do a single slope of the roof and basically cut out the eve cost.
You can frame a whole house with nothing but 2x4 but it s easier to do a shed as you won t need engineering probably.
An syp rafter can span 11.
Structures such as sheds or barns can be frames with rafters every 24 again make sure to consult local codes.
If you live in an area that requires a shed roof rafter to support a heavy load then an spf rafter can only span 7.
Makes construction easier too.
Both of these are for light roof loads.
I think you will be fine with 2x4s so long as they are closer than 48 apart.
It is always better to have a large rafter rather than be concerned with a sagging roof.
If your project had a rafter length of 8 or less a safe and strong method is to use 2x8 framed 16 on center.
You can use them for roof floor and even wall framing but few sheds will need trusses for walls.