Is authenticated encryption basically a lockable box?
No.


Yes, by choosing an authenticated encryption scheme with a known $\:I\hspace{.03 in}V\hspace{.04 in}||\hspace{.04 in}C\hspace{.04 in}||\hspace{.04 in}tag\:$ and $k_{\hspace{.02 in}0}$ and $k_1$ such that decrypting $\:I\hspace{.03 in}V\hspace{.04 in}||\hspace{.04 in}C\hspace{.04 in}||\hspace{.04 in}tag\:$ with $k_{\hspace{.02 in}0}$ and $k_1$ yields different outputs, neither of which are $\perp$.

These three links describe a black-box construction of authenticated encryption from one-way functions. $\:$ On the other hand, there is no known construction of non-interactive commitments from one-way functions, and this paper declares, "We rule out the possibility of black-box constructions of non-interactive commitments from general (possibly not one-to-one) one-way functions." However, Naor's scheme comes close.

The only candidate constructions of non-interactive commitments that I'm aware of either use a

$\:$ (1) key agreement scheme with sufficient completeness (this is the standard way to do it), or
$\;\;\;\;$ 
$\:$ (2) family of injections given by tuples of multi-variate polynomials over finite fields, or a
$\;\;\;\;$ 
$\:$ (3) keyless CRHF (these cannot be secure against non-uniform committers), or a
$\;\;\;\;$ 
$\:$ (4) hitting one-way function (in addition to presumably being only computationally hiding,

$\:$ these are also not known to be binding against (uniform) efficient committers)

.