You seem to be asking what the reason is for many papers on $p$-adic Selmer groups to assume throughout that $p > 2$: is because the case $p = 2$ is less interesting, or because it is more difficult?

The answer is definitely the latter. For many theorems concerning p-adic Selmer groups, there is an argument that works to prove the theorem for all sufficiently large primes, but $p = 2$ (and sometimes $p = 3$ as well) present extra difficulties. So it is common to deal with the "generic" cases of large $p$ first, and subsequent papers can then fill in the small primes later. See for instance [this paper][1] by Flach, which is devoted to filling in the $p = 2$ case of a theorem proved by Burns and Greither for $p \ge 3$. 
  [1]: http://www.math.caltech.edu/~flach/mainconjecture-at-two3.pdf