wouldn't a ground supported slab, if possible, be a more energy efficient design .
Vent BB floor means potential designed in unnecessary heat loss

Easy then.

You could consider filling the entire void with polystyrene beads then there would be no void and so it would not need ventilating. This would cost more initially but would save the cost and hassle of air vents.

In all cases you will need a floor air tightness barrier to stop unwanted draughts entering your home.

I've just finished our slab and the timber frame is now being built

I had the Tetris system and UFH installed into the slab, which seemed like a good idea at the time but now I'm not so sure

It is difficult to get a snug fit between the ground beams and even harder not to leave gaps between the insulation and the closure blocks. I spent a lot of time filling the gaps with expanding foam

Even though everyone said that it was not affected by water I didn't feel comfortable about that (water trapped in the very small gaps will not evaporate in my view even though the cavity underneath is ventilated)

Black plastic sheet went on top with ufh on top of that. Problem is the plastic is perforated by the ufh clips (no problem per the manufacturer) and needs careful taping - otherwise again water ingress when in rains

Mesh goes on top of the heating coils (support it as much as possible and be very careful of any sharp edges touching the pipes and any movement of the mesh as the concrete is poured) then concrete poured on top. However careful you are the mesh and pipes get some pretty rough treatment by the groundworkers

During this time the manifold needs support and protection (hard when concrete is being poured around it) and of course it is susceptible to damage, theft etc as it is basically unprotected throughout the remainder of the build

And to cap it all the timber frame erectors were told that no nails into the floor then promptly nailed their cross braces into it!

I personally think that Tetris and the others look very simple to install in their computer animations but in practice are on the limit of what the heavy trades such as groundworkers and the weather can throw at this method of construction