Yes, it's a terrific stepping stone to providing premium services as well. You may find you and your team naturally gravitating to a core competency that really interests you. Such as voice services, media streaming, etc.
Just be aware of the potential liabilities. Clearly demarcate ownership of all assets in contracts. As well as any obligations for future services. At some point a client may decide they can save costs by "cutting out the middle man" and negotiating directly with you!
You might read up on http://www.appaftercare.com/, the guy who started it is named Einar Vollset. It's a similar idea (I think) and he has published a lot of material about getting started with it.
What kind of pricing are you thinking of, for say, 20 hours / week remote help in maintaining an existing system for a small shop? (LAMP / AWS stack)
Spending your days trawling through other peoples uncommented, undocumented, and ineligible code sure is soul-destroying.
Good luck with this. We have been working on something similar for Mobile applications.
There are two aspects we are focusing at this moment:
A.) Rescue Projects: Projects which other team has messed up or left unattended. We take over these projects & ship the same in reasonable shape.
B.) App Fixers: We have created a website specifically for App Maintenance & Upgrades. https://app-fixers.com (We cover maintenance contracts, App Store upgrades, OS Upgrades related changes, Screen Upgrade related changes)
Start talking about this in the community. You will receive great contracts soon :) Cheers