It started with corporations. It's far "cheaper"—in how things appear on a balance-sheet—for corporations to subscribe to services, than it is for them to buy software at retail. "Convert CapEx to OpEx" is the keyword-phrase to chase for this. It's the same reason hardware sellers like Apple have leasing programs: they're mainly for corporations, and just coincidentally there for individuals.
Do note that the big conversions to SaaS models in recent years—Adobe Creative Cloud, Microsoft Office 365, etc.—are of products where 90+% of the revenue already came from corporate buyers rather than from individual consumer licenses. That the SaaS model also does something-or-other to drive consumer income is cute, but kind of irrelevant to the product managers who are making these business-model decisions.
Do note that the big conversions to SaaS models in recent years—Adobe Creative Cloud, Microsoft Office 365, etc.—are of products where 90+% of the revenue already came from corporate buyers rather than from individual consumer licenses. That the SaaS model also does something-or-other to drive consumer income is cute, but kind of irrelevant to the product managers who are making these business-model decisions.