Imo this is a bigger cultural issue than solely deodorant, though it's quite possible deodorant marketing had a role in creating it. I've noticed Americans tend to be more worried about perspiration than others who live in similar climates, to the extent of entirely avoiding outdoor activity in hot climates during the work day, lest they return from lunch break sweaty. In Greece people aren't really similarly worried about walking 5 blocks to grab lunch, even if it's hot out.