Why aren't there any birds or mammals that use toxins the way that certain reptiles and insects do?

There are several.
https://www.bioexplorer.net/poisonous-birds.html/

Humans are toxic in slightly different but highly effective ways also. ; )

there’s quite a list. https://en.wikipedia.org/wiki/List_of_venomous_animals

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I was surprised to see platypus included

My husband sometimes is toxic. LOL. He calls it repelente when I complain.

Several mammals are:
shrews (Order Eulipotyphla),
platypuses (Order Monotremata),
vampire bats (Order Chiroptera),
lorises Order Primates)

Amongst the birds:
pitohui and ifrita birds from Papua New Guinea,
European quail,
spur-winged goose,
hoopoes,
bronzewing pigeon,
red Warbler