It doesn't distribute the load, but it does reduce the shock loading for the floor underneath by a considerable amount (due to the rubber 'damping' the drop of the plates).
You'll be better off with the plywood and rubber idea that you've suggested, but keep in mind what a few people have noted - the difference in heights. Those plates are going to sit around 30mm+ higher than your feet.
Another option; more stable, but bulkier, (and a way to bring that difference down to around 15mm) if you aren't handy (and don't want to try and become handy) is to purchase a sheet of ply 2400x1200, get it trimmed down to 2000*1000, and just glue half of a 1m*1m rubber matt to it.
You'll need to use something like Fulaprene 303 or Soudal Fix All for sticking down the mats - most generic hardware adhesives (Nailbond, Liquid Nails, No More Nails, Constructions Adhesive) won't have both the flexibility and adhesion for durability under those mats.
So;
1x Ply 2400*1200*(15-18)mm (cut to 2000x1000mm)
1x Rubber Matt 1000*1000*~15mm (cut in half)
1x Fulaprene 303 or Soudal Fix All
You should get away for around $100, and it'll be darn easy to construct. Stanley Knife (preferably solid trapezoidal blade not a snap-knife), and a Caulking Gun are the only non-consumable tools that you'll need.