Subatomic particles are still constrained by the same speed of light as larger objects. As you scale up the speed by which this recursive universe operates in, this limit becomes more and more significant, and fewer interactions can occur in the relative unit of time.
To put it another way, if this super-universe were to use solar systems as atoms, the speed of light would mean their timescale would be in the billions of our years to their seconds. This is derived from the picosecond delay of forces acting between our atoms and scaling up to the solar system “atoms” that make up our galactic neighborhood (10-100 light years apart). So solar systems couldn’t be atoms on this timescale because they would do little but coalesce some of the intergalactic medium and die in seconds.
It’s possible, but the theory assumes we’re operating within the same physics, just different scales of time and space. Supposing there are other universes with their own laws of physics is rather arbitrary, and you could literally argue anything :)
I would argue a universe as a unit is a terrible candidate for an atom for a super-universe since our physics assumes it is a closed system. It would be neat if we weren’t bound by the heat-death of the universe and somehow low entropic states could leak back in. But that is all pure speculation and it cannot be proven or disproven from a scientific point of view.