Cost is the most obvious reason to stick with the lower level medical. Higher classes of medical certificates need to be renewed more frequently, which means more frequent trips to the aviation medical examiner. A third-class medical certificate, which is all that you need to exercise the privileges of a private pilot certificate, is good for three years if you get it before you turn 40 and for two years after you turn 40. A second-class medical certificate is good for only one year if you are using it to fly as a commercial pilot certificate. And a first-class medical certificate has an even shorter lifespan-only six months if you are using it to fly as an airline transport pilot.
There are provisions for using a higher level of medical certificate than is necessary for the type of operation being conducted. For instance, you only need a second-class medical to act as a commercial pilot. If you happen to hold a first-class medical but are flying as a commercial pilot, that medical has the same duration as a second-class medical, making it good for one year for those operations. That same first-class medical could be valid for as long as three years if you use it to fly as a private pilot.
But, even if you plan to get a second-class medical certificate and use it to fly as a private pilot, that higher class certificate can cost you more money. The examinations for a first- or second-class medical certificate are significantly more involved than those for a third-class medical. As a result, medical examiners generally charge more for a first-class medical than they charge for a third-class medical. Additional tests may also be required for additional fees.
Of course, the added expense of obtaining a higher classification of medical certificate does not necessarily mean that you shouldn't go ahead and apply for one. Many ab initio programs require that new students pass a first-class medical exam before they begin training. This helps ensure that students won't spend months and thousands of dollars on training only to learn that they do not qualify for the necessary medical certificate. Other training programs and employers may also require pilots to earn and maintain the highest level of medical certificate before they start classes or begin a new job.
If you apply for a second-class medical certificate and are denied, you may decide that you want a third-class certificate instead. In that case, you don't need to have a new exam, but you do need to request reconsideration and submit new medical information to support that request. That may mean additional tests from another doctor, and again, additional cost.