Oberth's are really research/survey ships, they're also not the toughest ships out there and are vulnerable to hostiles, so they wouldn't be ideal for a deep space exploratory mission, IMO. Going out to study something previously discovered by another ship, yes, but not really doing it themselves.
Also by the looks of things they are very old and are getting replaced with the Nova-Class.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)