We're the polar opposite. AppleCare is great and all, yet we find that almost all damage to iPads is the result of physical damage. We can replace screens and other parts here from third party vendors. It's far cheaper assuming you've got the time/staff to manage that.
I believe that we find parts from a variety of vendors such as: etech.com (ifixit.com is a little pricey)
We've actually gone down both roads. For our first deployment, we went with AppleCare on all devices and submit any physical damage to Apple. Unfortunately the cost was high at $99/unit plus the $50 deductible on top of that. The best part about going through Apple is we haven't had to deal with any quality issues, every device is automatically swapped out for new-condition refurbished unit. We have had rolling DEP issues on the replacements but thus far, all of them have been resolved.
For our second round, we decided to try a local repair company - we automatically saved around $35k by forgoing AppleCare but we have had a lot of quality issues. Apple doesn't provide any parts to 3rd parties and as such, any replacement parts used are either pulled from other broken units or are knock-offs. Just for the quality issues alone, we probably won't go this route again.
Apple provides out-of-warranty repairs for physical damage, but it's pretty costly at $200-$380 depending on the model and issue.
Consider having your bean counters do a cost analysis. Apple's repairs can be costly out of pocket per unit but in many instances your total cost is significantly less than Applecare/Applecare + depending on the number of units your organization has.
We are an SSO and I do some repairs here but iPhone/iPad I simply facilitate mail in repair. I don't have time to be doing those repairs.