According to https://code.google.com/archive/p/zawgyi/wikis/WhyUnicode.wi..., there appears to be a mismatch between the corresponding code points of Zawgyi and Unicode. So changing the font used for rendering could conceivably result in corrupt text.

From the article it seems that Zawgyi rendered various Unicode codepoints (some of them reserved for the Burmese script and others from other scripts) in the order they appeared graphically. Although Burmese usually puts the vowel in the front of a consonant-vowel cluster, Unicode probably has it so that the codepoint corresponding to the vowel is encoded after the codepoint for the consonant. They're migrating by using a font that renders based on the Unicode order and keyboards that type in that order.

That's just what I got from the article and I have no other knowledge of the Burmese script so I may be wrong.

https://frontiermyanmar.net/en/features/battle-of-the-fonts (mentioned in the article being discussed) is much clearer.

Short version: in Burmese, the form a character takes depends on context. Zawgyi ‘solves’ that by having separate code points for the different forms, requiring the user to pick the right variant. The Unicode way is to make the font and the (font + font renderer) pair smarter, just as Unicode renders “é” instead of the two code points “e’”.

Zawgyi also, necessarily, uses Unicode code points assigned for other characters to encode the variants.