No success either with legendfonthalign attribute.
A workaround is to left-pad the labels beforehand and use a font such as Courier so that the columns of characters are consistently aligned.
Computer Modern legends are not perfectly aligned but look better:
using LaTeXStrings, Plots; gr()
default(fontfamily="Computer Modern")
n = 3:2:23
x = 0:0.01:1; y = [3*n*exp.(-(n*(x .- 0.6)).^4) for n in n];
labels= permutedims(string.(n) .* " [s]")
n = maximum(length.(labels))
plot(x, y, label=lpad.(labels,n), legend=:outertopright) # legendfont=font(6,"Courier")
plot!(xlabel=L"CVE",ylabel=L"Density")
Legend with Courier font:
Legend with Computer Modern font:
