I'll 'weasel word' my answer just short of a b/w 'yes' or 'no' on which size 1 bys to pick, and pass along what I learned...
1. Someone here used only 1/2" Ply for their Bed Support. It worked fine. What's happening in what I built is the Ply is simply spreading the load between the 1 bys WHILE adding intrinsic Ply strength, obviously.
2. This same effect is true with the 1 bys. The Load is spread to several of them simultaneously [Glue helps achieve this]. Glue also makes this Assembly act like one side of an Engineered Lumber Joist; stronger than you might intuitively think... And, so, the question is 'will
3 or 4 - 1" x 4"s [not just 1] support the load put on them. They will. Choose 1 bys w/o Knots, or put the Knot at the bottom of the span.
3. We all sit up and on the edge of a Bed [concentrating the load momentarily], and then get up. However, this doesn't happen at the 'Head' end. So, toss out the notion that each 1 by span has to be uniformly spaced at, say, 12". The 'Body Mass' part of the Bed is where the true support has to be. Head and Feet; not so much. So, perhaps 16" on center for the 1 bys is fine there. Put in more 1 bys for the Body Mass: Shoulders to Hips. Double up 1 bys at the Foot end only if folks are going to sit there. Keep an open Mind, and tweak where you put the 1 bys. We're not building a Floor here to hold a Piano!
4. If you can, and want to, try a mock up. Put some 1 bys near the ground on some scrap Lumber. Nail the ends with a 1 x 2 to keep them from falling over, Dominoes-style. Put even a scrap a 1/4" of Ply [or OSB] on them and lay on it. Tweak the Design as necessary...
Once you choose the Bed Frame Lumber specifics, realize that Glue will help in that it makes the entire Assembly a uniform item that really spreads the Load over several pieces. Think 'Airplane/Glider Wing' or 'Bird Wing': light but strong.
As with Lumber Tables for Building Floor Spans, an assumption here is that there will be some Bed deflection when you lay down [more than at Home]. That's fine. All you want is deflection reliably short of Bed cracking and failure, right?

I HIGHLY recommend a Mock-Up Model, first, to avoid disappointment and blowing useless $$ at the Big Box Store. Do a partial Mock-up and lay cross-ways on it for testing.
I WAY over-built an old Bed Decades ago and we still giggle when we have to move that monster between Rooms occasionally. 2" x 10" Frame; 1/2" Ply; 4" x 4"s to hold up the Ply center seam; total overkill vs. simply holding up ~500 lbs. over the sq. footage of a Queen or King Size Foam Mattress [2 Humans + 1 big Dog]. If a Ply seam or two is necessary, put it a foot from the edge; not in the Bed center.
Rather than using Deck Hanger Hardware, or weakening the ends of the 1 bys - due to screwing into them - I notched out the bottom of my 1 bys. I rested them on a 1" x 1" glued and screwed to the bottom edge of the visible Walnut Wood Bed Frame. That made this entire 'Glider Wing' Mattress-support Assembly invisible from the Bed exterior; no Screws marred the finish. You've already got them, so the Hangers are fine, of course...
To be very conservative, consider 1" by 6"s. Recycle the space between those 'deep' 1 bys to store Gear. Alternately, consider 'more' 1" x 4"s with less spacing on center in the Body Mass area if Bed Frame depth is an issue.
If you've got the 1/2" Ply, use that, obviously. My comments are 'Blue Sky' Design considerations for those really wanting to trim down TT or CT weight incrementally. 1/4" Ply worked great for me for several 6'-wide King Beds w/Foam Mattresses.