optimize bloated PNG files

I want to allow my users to post large dimension PNG files for drawings to maintain quality, but I have a new problem with new devices where people are posting bloated ridiculously large screenshots as PNG. Some users are posting screen captures of their screen that can be 500 KB - 1 MB that can be reduced to 75 KB by simply saving as a jpg.

Is there a way to force the bloated PNG screenshot files to be well-optimized while still allowing users to post quality drawings as PNG without losing the quality?
 
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