I'd appreciate any advice on this. I have acoustic-electric guitars and an electric guitar (with a small practice amp). I would like to buy one amp which will work with both types of guitars. I am currently considering an acoustic amp. How would it sound if I ran the electric guitar through an active direct box first, and then ran the balanced signal from the direct box into an acoustic amplifier? I don't use distortion. I just want a clean, full sound. I also want an amp which produces a balanced xlr signal so I can run it into a p-a system. That feature is usually found on acoustic amps - for example the $200 fender acoustasonic 40w amp - but not on electric guitar amps in that price range.
If you don't use distortion, then you absolutely can use an acoustic amp for electric guitar too. An acoustic amp is essentially just a PA-style general-purpose speaker in one chassis together with a good preamp and useful EQ controls. It sounds very similar to a straight DI into the console, but with more tone control, incl controls that help avoid feedback. So to judge whether the general sound is ok for you, try how you like your electric guitar plugged straight into a high-impedance input of an audio interface or active DI box.
In practice (i.e. a musical setting), electric guitar without an “electric amp” tends to some out crisp, detailed, but may also appear somewhat thin, hollow or bodyless. For a full sound, you'll probably at least need to tweak the EQ a bit; it can also make sense to add a compressor pedal or a tube preamp (you can get cheap ones that are intended as mic preamps, e.g. ART TubeMP or Presonus TubePre), to get it more in direction of a normal electric amp. Or taking it further, you can always take a digital multi-effects board with cabinet emulation, then you can actually run any electric sound you want over that acoustic amp.
Another concern might be loudness. It's fairly obvious that an 8" acoustic cube can't produce as much noise as a Marshall full stack... but practically speaking, this is actually not as much a problem in a live setting anyway. If you don't hear yourself good enough, it's usually better to get the amp closer to your ear not making it louder. If the others don't hear you loud enough, well, that's what the PA / monitors are there for!
In summary, yeah, I recommend getting an acoustic amp. Just pick a decent one, not sure if the Fender Acoustasonic is very good. As with many things, it's best to try it yourself with a couple different models before buying.
Looking at it from a more technical perspective: any amplifier must have an input impedance compatible with the output impedance from your guitar. A mismatch there will lead either to severe signal loss or, at the other end, dangerous overload. In particular if you were to send a high-ish voltage output from a powered guitar to an amp expecting much lower-voltage signals, SomethingBad(TM) could happen.
Other than that, it is purely a matter of the amount of amplification and the linearity of response (that is, overdrive, pulse shaping, roll-off filters, etc. are deliberate nonlinear preamps) desired.