Totally depends on the market. For example, most e-commerce companies are very comfortable using SaaS and Javascript snippets nowadays, but if you try to pitch SaaS to a bank, they'll just laugh. Over time, I think more companies will get comfortable with SaaS, but it will take years.
If you're pitching SaaS to an industry that doesn't usually go for it, it sometimes it helps to avoid PII. Even banks are somewhat open to using SaaS for products that don't touch customer's names, transaction info, etc.