The root cause here is the DNA double-strand break induced by Cas9, and the ensuing DNA repair processes that occassionally produces large deletions (the paper reports two thirds or 32/48 were less than 50 bp and 21% or 10/48 were greater than 250 bp). This has been largely known by the DNA repair community for 20+ years.
Currently, our most powerful genome editing techniques rely on CRISPR's ability to induce double-strand breaks, such as HDR (for inserting designed sequences, used in gene drives for instance) and NHEJ (for knocking out genes, used in all current early-phase therapies under development). However, a double-strand break is among the most traumatic experiences a cell's genome can experience. We're currently taking advantage of the cell's freak-out attempts to repair its DNA for genome editing purposes, but the process is noisy and produces highly variable and stochastic outcomes. HDR, for instance, has a baseline efficiency of less than 20% in many cell types and conditions of therapeutic interest. Many papers have shown dramatically increased HDR rates at the expense of altering the cell's DNA repair pathways, but these were never going to be humanity's dominant therapeutic approach -- messing with DNA repair is dangerous and closely linked to cancer.
The holy grail is a genome-editing tool that is highly precise, with no off-target effects (edits only exactly in the genome where we want) and highly precise on-target effects (results in the same change everytime we apply it) and flexilbe (many designable changes). The messiness of cellular DNA repair is a major challenge to the second goal. The scientific community has recognized this and has been working on CRISPR-related genome-editing technologies that rely less or not at all on inducing double-strand breaks, thereby skipping the messiest part of the genome-editing process.
One example is base editing, where the endonuclease domains of Cas9 are disabled (called dCas9, sometimes explained as "dead" Cas9), and alternative enzymes that transform nucleotides (such as C->T) are attached to dCas9. In this setup, dCas9 provides the "homing" targeting while the attached enzyme enacts the editing without inducing a DSB. As it stands now, base editing is very exciting, but further work remains to develop base editors for all possible nucleotide transformations (a -> b for all a != b in {A, C, G, T}); it's not as flexible as HDR.
I do want to note another therapeutic domain of ex vivo therapies, where the messiness of DSB-associated genome editing strategies is much less of an issue, since cells can be screened after editing in vitro to control which genotypes we're inserting back into the patient.