Number of pillars per layer

Definitely better to use 4 pillars, rather than 3. Otherwise, tables would mostly be designed with 3 legs if it were more stable than having 4.

Make sure you put another 4 pillars in your 10" to support the 8" on top, don't just put one cake on top of the other since it could collapse under the weight.
 

The traditional camera support is a tripod. Three legs. Studio television cameras are often mounted on pedestal dollys, but they still typically have three casters.

Light stands, music desks, candle stands, milking stools, and so forth typically have three legs.

No matter how irregular the ground, no matter if the legs aren't the same length, a 3-legged support will always be stable, if not necessarily level.

A triangle is the one polygon that can't be distorted without changing the length of one of the sides.

On a lathe, a 3-jaw chuck is self-centering on round stock. Which is why drilling chucks (except for 2-jaw bit-brace chucks designed for square-tanged bits) almost always have 3 jaws.

But on the other hand, 3 pillars might not provide enough support. Indeed, depending on the situation, 4 might not be enough, either. And presumably, with cake pillars, you're not going to be compensating for uneven ground or pillars of different lengths.

The stability does not come from the pillars, it comes from the dowels inside the cake tiers.  These have to be cut true and all the same length for each tier.  Get your husband to use his mitre box for your benefit.  Please read the linked pages from this index:

http://www.wilton.com/cakes/tiered-cakes/

I think the Wilton plates LOOK unstable because the pillars end up near the outside edges of the cakes.  I would personally have the four pillars in closer to the centre.  But let me tell you, the Wilton pillar-plate system survived my sports-playing brothers attempts to demolish my cakes-in-progress, so they are definitely good.

The other advantage of the Wilton and SPS plates is the nubs that keep the cake tiers off the table for secure grip and easy moving.  The nubs lock into the pillars or hollow supports, and assembly onsite becomes simple.

So I say out of my experience, that four pillars are good.  Your cake design will also determine whether you should have four or six pillars...