The "standard" Morava E-theory $E_n$ (at a prime $p$) is typically defined using the so-called "Honda formal group law", the unique FGL $\Gamma_n$ over $\mathbb{F}_{p^n}$ satisfying $[p]_{\Gamma_n}x=x^{p^n}$. The story is that we take the universal deformation of $\Gamma_n$, which is Landweber exact, and lift it to a complex-oriented $E_{\infty}$-ring with an action of the Morava stabilizer group $\mathbb{G}_n=\operatorname{Aut}_{\mathbb{F}_{p^n}}(\Gamma_n)\rtimes\operatorname{Gal}(\mathbb{F}_{p^n}/\mathbb{F}_p)$. Then this is a pro-Galois extension of $L_{K(n)}\mathbb{S}$ with Galois group $\mathbb{G}_n$, and we can use this to obtain a fixed-point spectral sequence and so on.
Except...the Honda FGL is not unique in this regard. Given any formal group of height exactly $n$, its universal deformation will yield a presentation for the formal neighborhood of the height $n$ formal groups in $\mathcal{M}_{fg}$, and we'll get an associated pro-Galois extension and an equivalent fixed-point spectral sequence. The multiplicative structure on the Lubin-Tate spectrum will be different and we'll get a different description of the $E_1$ page of the FPSS, but ultimately this just yields a different presentation of the same object (the $K(n)$-local sphere).
So, why do we use the Honda formal group? Is it for historical reasons? Is it for computational convenience? Or is there something deeper going on with the Frobenius map? I was until recently laboring under the misapprehension that there was something pertinently "universal" about this formal group, but now I'm wondering if there's any reason not to replace it with some other one (e.g. a supersingular elliptic curve at height $2$).
