Package to use utf-8 characters in plain LaTeX?

Question

I’m discovering the joy of typing directly UTF-8 characters easily on my keyboard (thanks bépo and/or XCompose), and I’d love to use them to write more readable LaTeX, without resorting to using LuaLaTeX. For now I need to manually define all my characters (thanks newunicodechar), but I’d love to use a package taking care of this for me automatically.

Is there such a package that I missed, or should I create my own?

MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{newunicodechar}
\newunicodechar{α}{\alpha}
\newunicodechar{β}{\beta}
\newunicodechar{⊗}{\otimes}
\newunicodechar{⊕}{\oplus}
\newunicodechar{∀}{\forall}
\newunicodechar{ℕ}{\mathbb{N}}
\newunicodechar{ℤ}{\mathbb{Z}}
\newunicodechar{⩾}{\geq}
\newunicodechar{∈}{\in}
\newunicodechar{∃}{\exists}
\newunicodechar{∧}{\land}
\newunicodechar{∨}{\lor}
\newunicodechar{⇒}{\implies}
\newunicodechar{½}{\frac{1}{2}}
\newunicodechar{²}{^2}
\newunicodechar{ˣ}{^x}
\begin{document}
$∀ x ∈ ℕ, ∃ y ∈ ℤ, x ⩾ y$
\begin{align}
  (A ⊗ B)(C ⊗ D) & = (AC) ⊗ (BD) \
  α ⊕ β          & = β ⊕ α
\end{align}
$a ∧ b ⇒ a ∨ b$
$x² ⩾ ½$
\end{document}