Yeah, burst mages are not overly prevalent bot lane but I feel a lot of their supposed "dominance" comes from how frustrating they are to face in lane.
Getting clipped by a Zyra snare in the current meta usually means death unless both your flash and heal are up. Getting clipped by a brand W will hit for over a hundred damage at level 1 and that scales up fast in laning phase. Sure you can "just dodge them" but it's not like you can magically flip a switch and never get hit by a skillshot ever again.
They out trade everyone unless they're completely stupid and punish going for CS hard. Theoretically you can beat them 2v2 with an engage tank, but a lot of low elo players aren't coordinated enough to actually execute a good 2v2. You can also play safer and wait for ganks, but "play safe" is unheard of in lower elos and no jungler ever seems to understand that brand/zyra will
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Almost always pushed to our tower
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Is super immobile
I know this because I play in gold and with lower tier players on a team (as in, I play premade with silver or worse players for a tournament). As a result unskilled players get the idea that they're unstoppable.
Brand/Zyra are the only two I've ever had that much of an issue with. Lux is a trashball support against anyone with a brain and same with Xerath because their utility is low and they're too reliant on gold for stats.
but even then, the "good" mage bot laners fall of late game compared to a "real" support (unless people straight int them)