Too much vertical blank space for unbalanced math expression inside big delimiters

Question

A recent post on Math SE reminds me of an old issue as titled, shown in the screen grab below in case it is edited or deleted. There are several other issues with these few lines, but I'd like to just focus on the vertical white space inside the brackets.

Clearly the problem is partly inherent to the math expressions themselves being unbalanced in the sense that it is a big exponent on top of a small base, and one can certainly do something like \exp\Bigl( # \Bigr). Nonetheless, one can imagine situations where such "proper" formulations are not feasible.

I vaguely recall years ago dealing with this problem and solving it. However right now it seems my memory is faulty. Somehow I can find only a trick bypassing the issue via bmatrix, this using a box and vcenter, a package deal humorously named nath that's incompatible with amsmath, and another forcible practice deemed ugly (by the answerer Phelype Oleinik) using fixit from here.

It appears this cannot really be solved by smash (except in certain cases of inline use) since it defeats the purpose of having automatic sizing delimiters.

This seems to me like a basic thing that can be dealt with easily and "properly" without tricks like the aforementioned use of a matrix or a full-blown fixit.
In light of David Charlisle's comment (about staying on math axis or not), I'm working on refining (and reframing if necessary) my question.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
E\left[e^{-\frac{2\gamma^2}{a^2X+b^2}}\right] \neq E\left[\smash[t]{ e^{-\frac{\gamma^2}{a^2X+b^2}} } \right]^2
\end{equation*}
\end{document}

Answer 1

I wouldn't rely on the matrix trick here: The terms in the numerator and denominator of the e^{-\frac{...}{...}} expression will still look miserably compressed.

Instead, I'd replace with e^{...} notation with \exp(...) notation; see the second line below. In addition, if the formula occurs in an inline math setting, I'd replace the \frac{...}{...} with inline-fraction notation, i.e., .../.... Oh, and don't overuse \left and \right.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\E}{E} % expectations operator
\begin{document}
\begin{align}
E\left[e^{-\frac{2\gamma^2}{a^2X+b^2}}\right] &\neq 
E\left[\smash[t]{ e^{-\frac{\gamma^2}{a^2X+b^2}} } \right]^2
\[2ex]
\E\exp\Bigl(-\frac{2\gamma^2}{a^2X+b^2}\Bigr) &\neq 
\E\Bigl[\exp\Bigl(-\frac{\gamma^2}{a^2X+b^2}\Bigr) \Bigr]^2
\[3ex]
\E\exp\bigl(-2\gamma^2/(a^2X+b^2)\bigr) &\neq 
\E\bigl[\exp\bigl(-\gamma^2/(a^2X+b^2)\bigr) \bigr]^2
\end{align}
\end{document}