That's a question I asked myself as well, since I want to use shotguns and other short range, high number of shots weapons as breaching weapons. Once you look into it, aliens actually have very low armour values most of the time.
Just looking at Front Armours (since that's usually the highest), it barely goes above 50 (gazers, ethereals, sectopods) and usually 35 looks like a lot (Cyberdiscs have 34, mutons ~30), with 10-20 looking like the normal range.
Most tough aliens indeed seem to fall in the "low armour, high HP category". ~10 armour/70 health for anthropods, ~30/140 for mutons, ~15/65 for reptoids. Regular/weak aliens have 5-15 armour and ~40 health. The only balanced aliens are gazers (~70 armour and health) and ethereals (~50 for both).
By opposition, XCom personal armour is already 50 for front armour, 100 for power armour! The MiB also has more armour than health, because they use similar armours as XCom.
The FMP shotgun type weapons indeed have damage issue, with the plasma caster capping at 35 even 5 hits will do little damage. That's especially true for aliens shooting at XCom troopers wearing even personal armour (70% chance of no damage for a hit, 1-20 damage if you "roll" high against personal armour with EU damage rules and 95% chance of no damage with TftD rule, up to 3 damage).
Bringing the plasma caster up to pistol damage (~50) already could be huge improvement and would help the aliens too. If a plasma pistol can do 50 damage 3 times with an autoshot, it doesn't seem outlandish that a weapon designed for short range mayhem could do the same at the cost of long range capabilities, but that's for Solarius to consider.
For the endgame armoured aliens (Mutons, Gazers, Ethereals), I think it makes sense that you would need to bring heavier weaponry. Heavy Laser/Plasma rifles work pretty well with their ~80 damage. Afterall, you don't destroy a tank with one million pistol shots, you use one AT missile, it's similar in this case: You need some extra punch.
