Trapdoor snails have Opercula (the 'trap door') that they can close like a manhole cover and any and all appendages of your newt could get stuck and damaged, resulting in stress at best, and infection and death in worst case.
In my opinion, a good algae-eating snail to coexist with caudates is the Nerites sp. This is a marine type of snail that is very adaptable to fresh water. They will lay lots of eggs but they won't hatch because they need salt water to do so.