Is it the accepted view that the electric field is not quantized?
It is accepted that electric charge is quantized: proton = +1, electron =-1, neutron=0. Quarks have fractional charge: 2/3 or 1/3, but you cannot obtain an isolated quark at anything like normal energies.
As you move away from the quantized charge, the electric field intensity decreases as an inverse square law.
Since distance is not quantized (or, at least, the Plank length is so small that we can't measure it), then the electric field is not quantized.
The rest mass of a proton or electron is quantized, but their relativistic mass is not. The gravitational field is not quantized.
I do not like to see terms such as infinite and infinitesimal in a scientific discussion.
In formal mathematical terms, you would say "As distance from the proton approaches infinity, the strength of it's electric field asymptotically approaches zero.".
But this is a reasonable shorthand: "for a free charge, the electric field extends to infinity (though at infinitesimal strength)".