Your argument would be compounded with both penalties. You should ask yourself the question "why am I trying to select the optimal combination and what benefits are there over the common choice of 0.5 for alpha". I cannot comment because I don't have a rep of 50

I think in general practitioners will fix alpha=0.5 when fitting an elastic net model, and use cross validation only to select $\lambda$. Searching over a grid can lead to overfitting even if your using cross validation. Nevertheless, there is an interval-search algorithm implemented in the c060 package will select the optimal parameter combination.