I think Bitcoin ATM and to safe money does not stand together. When a person uses it, he should be ready to pay extra. With Bitcoin ATM this extra is time. When you buy Bitcoin from exchange, getting verified takes time. Sometimes it is few minutes, sometimes it takes days. During that time prices can severely change. How ever I've got your point, using ATM to buy Bitcoin is expensive.
In my country every telephone number is bind to ID. You cant buy a shady SIM (probably could, but it takes time and you have to know where to buy it), or buy just a SIM at a shop. ATMs sometimes ask to enter a code from SMS as a verification of a deal. The fact that my personal data is collected by someone is what bothers me most.
If time issues prevent you from being able to use bitcoin ATMs, Remember that the Lightning Bitcoin Network is already available and Bitcoin ATMs of course take advantage of the Lightning Network to process transactions faster and cheaper. That won't be a problem.
However, for data collection such as SMS verification, which is required and must know your personal number and some other information (KYC) it becomes optional, you can use it or not. But if bitcoin ATMs don't use KYC there will be a lot of money laundering done. Currently, several Bitcoin ATMs in the UK have been shut down because they do not have permits and are indicated to be places for criminal transactions.
Thus, Bitcoin ATMs currently still need some development that needs to be integrated with user needs as well as regulation and security of Bitcoin ATM users.