Not a bad idea, but for me I actually prefer the pulldown on mobile because it doesn’t require me to type anything to scroll through and find the canned reply I am looking for. We have quite a few canned replies as well and it’s never been an issue for me.
I see you are using a prefix for organizing your canned replies - care to share about the system you are developing? I am struggling myself with organizing the canned replies to make them easy to find, especially when they are in different languages!