It's hard to see a subscription model for logo designs though. It's not like you need a new logo each month.
That time they could save is likely much more valuable than just the one time fee, and constant improvements and features for them could very well justify a nice recurring subscription fee.
http://www.thedigitaldesignco.com/graphic-design-subscriptio...
not exactly just logos but people seem to try and SaaSify everything.
But your two examples here seem exactly the kind of long-term customer relationships that benefits from SaaS. And may in fact be underutilized. These are high-touch, deep background kind of gigs, rather than impersonal service sites. I want to have an ongoing conversation about my task and I'm willing to pay a retainer++ for that privilege.