Smaller/cheaper.... but there's, what, a 1:4 step-up? ATs are great for 90%-110% ratios (size is 1/10th), even 1:2 ratios (size is half). Much over that the difference is minor.
Isolation... but the EL panel naturally "floats" and you won't be putting finger on it.
Knowing that there is no isolation, the transformer designer can skip inter-winding insulation, even interleave all turns, for best high frequency extension. In an LA-3 this seems moot: we seldom limit on >>2KHz overtones (listener's ears would burn even before the tape/MP3 overloaded).
I would guess the original used an AT because they had something suitable on hand, or the custom design was a penny cheaper as an AT. I'd figure it "unimportant" in a DIY build.
Note that any 2-winding transformer can be connected as an autotransformer, though with a different ratio. (600:10K 1:4 2-winding becomes a 1:5 or 1:3.)