Most students from non-accredited programs were already not competitive for APA-accredited internship sites, even compared to professional schools and diploma mills, so barring them from the match really wouldn't change things much.
Yes, some professional schools' match rates have increased, but it's important to not attribute it to programmatic changes or improvements to these programs. Instead, it's more likely a function of two phenomena:
1. significantly increased number of accredited internship sites, which decreases the competition.
2. increased use of captive internship sites by professional schools and other poor quality programs to game the internship match statistics, specifically so that they don't have to make changes to their programs (e.g., reducing cohort sizes, exercising more discernment in selecting applicants, improving the quality of didactic and experiential training, increasing research milestone requirements)