You actually brought up a good point. How hot does a deck get baking in the summer sun and how much temp does carpenters glue need before it gets soft? I guess the answer is: hundreds of strippers have been built using carpenters glue and they do fine. I tried to find some info on what temps are needed before the glue breaks down and its tough to find. Glue manufacturers don't want to talk about it. And our needs as strip builders is unique.
I know from experience with making guitars, Tightbond 0 is the most brittle and hard although I've built strippers using Elmers carpenters yellow glue with no problems. I have also read many glue test and depending on the wood and the type of test etc. no one brand or type is the absolute winner on everything.
Many instrument purists use Hide glue which actually is stronger than carpenters glue and if you heat it to remove a part for a repair, it sticks to hardened Hide glue great vs yellow carpenters glue does not stick well to hardened carpenters glue.