Although I'm not an expert on this, I will give it a shot. The "Certificate of Calibration" is essentially a statement of as found/as released quantitative information about how the instrument is performing at a given time. Establishing the interval is a separate issue.
For example, I am currently working on statistical evaluation of about 86,000 calibrations in my company's calibration recall database. This is based on NCSLI Recommended Practice method 3 (if I recall corrrectly - sorry, it's late on Friday afternoon). The interval is a statistical probability to a given confidence of how long an instrument may be expected to remain within tolerance. It may be lengthened when prior as received calibration history allows it, or may be shortened when prior history dictates that way.
The given users accuracy requirements, frequency of use, environmental factors, the "lemon factor" (if you have one bad one in an otherwise "good" population of instruments, it has a "lemon factor") and other factors can impact what the interval should be set to.
This is distinct from the Certificate of Calibration. Particularly if you send to the OEM or Third Party lab, since they don't have your internal data, it isn't fair for them to assign an interval. This may potentially create an undue increased risk of out-of-tolerance performance, and possible conflicts.
For (fictitious) example, suppose I have 100 Fluke 77 multimeters (no good or bad implications about Fluke 77; it's just a very common instrument). I've (fictitiously) been calibrating them for the last 10 years with an initial assigned interval of 12 months. After 10 years of history, I find that 5 of the meters have a higher out-of-tolerance history than the others. I research and find that these are used by a crew outdoors. They are frequently dropped, exposed to higher voltages, lay in the truck in the heat, and so forth. I've had to adjust that one little potentiometer in these five a few times, where I haven't ever adjusted any other in my entire population of Fluke 77's.
My recall system and calibration records state the assigned interval (which I statistically derived based on history - still, a fictitious example). However, I sent two of the bad meters back to Fluke, where they calibrated them twice. They sent back a Certificate of Calibration with them, but did not provide a due date, since it isn't appropriate for them to include that in the certificate. When I received them back from Fluke, even though I increased the intervals on all the remaining population to 30 months, these five are at 12 months, and 2 of them are at 6 months.
Hopefully this will shed some amount of light on the question. Have a good weekend. I'm going home.