Hi TR Houston,
You can read a little more about the different types of foundations or box springs and how they are usually paired with different types of mattresses in post #2 here.
It would be helpful to think of a foundation or boxspring as having 4 different properties or benefits and each of these serve a different purpose.
The first of these is flex. The flex of a boxspring (with actual springs) or a “semi flex” or “limited flex” wire grid foundation or a base with various types of flexible slats serves two purposes.
The first is to act as a shock absorber for some types of innerspring mattresses which can be damaged with sudden or more forceful “shocks” because the wires may bend and set in a bent position. Foam isn’t subject to this so it doesn’t require any type of shock absorber underneath it.
The second purpose of these more “active” support systems is to contribute some flex to the mattress which can affect the properties and performance of the mattress and is part of a “sleeping system” that includes the mattress and the box spring. If a foam mattress is too thick (usually beyond about 6" - 8" or so) … then the benefit of the increased give under the mattress would be diminished or even lost completely. In most cases … at least in North America … the layers in a foam mattress are designed to be “stand alone” in terms of how they feel and perform and the foam is designed to do all the work and only needs a firm and evenly supportive surface underneath it. In Europe … thinner mattresses are more common and the bases underneath them are often designed as an integral part of the overall performance of the sleeping system and it’s much more common to see more flexible foundations (often with flexible slats) under a thinner mattress. Even in North America though … you will find some manufacturers that design their mattresses to be used over a flexible boxspring which is an active and important part of the complete sleeping system (although again this is usually with thinner mattresses). There are also cultural differences between mattresses in different areas of the world which leads to some designs being more “familiar” (meaning they would sell more easily) than others.
If you test a mattress with an “active” boxspring that noticeably contributes to the feel or performance of the mattress in terms of PPP (Posture and alignment, Pressure relief, or Personal preferences) in a showroom vs the same mattress on a solid non flexing surface then it’s a good idea to purchase them together because your overall sleeping system will have different properties if you use the mattress on a different type of base with a different amount of flexibility than the one you used to test the mattress.
The second property of a boxspring or foundation is to provide a firm and evenly supportive surface for the mattress so that the mattress doesn’t hammock and sag in the middle and it doesn’t have to sit on the floor. The amount of surface area that physically supports the mattress can be important here because some types of foam (particularly more elastic and flexible foam like latex) will sink into any gaps more easily than foam (like polyfoam) which is stiffer and less elastic. In the case of a latex mattress the suggestions of having gaps that are 3" or less is to prevent the more elastic latex from sinking into the gaps over time. A little wider gaps (up to about 5" or so) would generally be suitable for a polyfoam base layer which is stiffer than latex (although smaller gaps would still be preferable and will be stronger and more evenly supportive). In the case of “wire grid” foundations which are usually called semi-flex or limited flex foundations then the wire grid has much less surface area than wider slats with smaller gaps and can also have some risk of latex sinking into the gaps in the grid (although they would generally be fine for a polyfoam support core). You can read a little more about this in post #10 here.
Third is ventilation under the mattress. The most supportive material under a mattress would be a solid surface (such as a sheet of plywood or MDF) that had no gaps at all but this would also provide no ventilation under the mattress which in combination with other risk factors could increase the risk of mold and mildew and dust mites in the mattress (see post #10 here).
Finally the last reason for a foundation is to add height to the mattress so that the surface of the sleeping system is at a comfortable height to get in and out of bed or that fits the bedframe or headboard or footboard you are using. In some cases a platform bed for example that has strong slats with smaller distances between the slats that are supported in the middle with legs to the floor may not need a foundation or boxspring at all.
In terms of the flexibility of a foundation or box spring … if the one you buy with your mattress has the same flexibility as the one you tested with the mattress the feel and performance of the system will be the same.
In terms of the amount of gaps and the supportive surface area of the foundation then the more “air” there is in between the supportive surfaces the greater the risk that the mattress will compress into the gaps in the longer term. With more flexible foams such as latex then the longer term risk would be greater but this isn’t possible to quantify exactly and the difference may be small depending on the total thickness of the mattress, the firmness of the foam, the type of cover and quilting on the mattress and on the foundation, the type of foam, the ratio of the supportive surface area relative to any gaps, and the weight of the people on the mattress. In other words there is a “range” of potential risk that could range from minimal to much greater.
The same would hold true in terms of the “range of risk” of a less breathable support surface and this would also depend on other risk factors as well (climate, temperature in the room, humidity, the amount of normal perspiration of the sleeper and others). By itself single risk factor may not be as important.
Catastrophic failure would be very rare on any suitable foundation although it may be more common on foundations that weren’t strong enough for the mattress and the people on top of it. I would be more concerned with the ability of a foundation to maintain a flat and evenly supportive surface over time and on any of the other risks that were involved with the type of foundation.
So overall the choice of a “suitable” foundation would depend on which of these functions were most important to the overall sleeping system and the other “risk factors” that were involved in each of them. The “norm” in the mattress industry is that different people will have different thoughts and beliefs about the risks or benefits involved in each choice but I would always want to know the specifics of “why” they believed what they believed.
Hope this helps but if I’ve missed anything let me know 
Phoenix