Is there a precedent for this kind of plan working? We have antitrust law but antitrust law doesn't actually prevent big firms from becoming big; we've had General Motors, Microsoft, Google, and others, all very large relative to their sectors.
You could imagine an absolute cap on the size of bank assets, so that above the size limit would-be loans and deposits are sent to a rival institution elsewhere by mandate. One implication is that banks won't have to treat their customers very well, since in a growing economy (we'll get one again, sooner or later) a lot of banks will be at the cap and will be turning away extra business. If different banks were perfect substitutes for each other, you wouldn't be seeing large banks in the first place.
A second question is whether ten little banks are safer than one larger, 10x bank. For sure they are if the problem is one bonehead manager at the bigger bank, but what if it's systemic asset price risk? The smaller banks could well be less safe. In a financial crisis, would you rather be a larger country or a smaller country?
I believe the plan would require very tight restrictions on off-balance sheet activity. Something like this may be coming anyway, and its rationale is understandable, but it is easier said than done. We would be requiring regulators to estimate the net "size" (it's debatable whether that word even applies; what is the "size" of a naked put?) of a bank financial position when banks themselves haven't been very good at doing that. A simple approach would be to ban all bank trading in derivatives but I believe that would increase bank risk more than decrease it, at least at this point.
By the way the 1927 McFadden Act banned interstate branch banking, in part to keep banks small, and economic historians usually consider that policy to have been a disaster which contributed to the severity of the Great Depression.