Cheap suspension cannot hold a candle to Big Apples. Too many disadvantages.
* Suspension is a LOT heavier than the weight penalty of BA.
* Cheap suspension is usually not adjustable, especially the damping, leaving you with a bouncy energy sapping ride.
* Cheap suspension will usually have poor tolerance, which results in sloppy frame movement. Very Bad.
* The unsprung weight of any suspension is much bigger than the unsprung weight of BAs, which is zero.

Then there is the cost argument. A bike cheap enough to fit an entry-level budget, will generally be of poorer quality than a same priced bike without suspension. More welds, more parts, more moving parts.

As for rotating mass, that is a red herring. The rim, spokes and hub are a much bigger fraction of the total weight especially in a cheap bike, than the few 100g of a set of big apples. Not to mention the vastly bigger amount of mass of the rider that has to be accelerated. Light wheels are of course nicer than concrete donuts but let's not lose perspective here while discussing the merits of BAs.

Big Apples are streets ahead. And don't be misled by the rather silly argument about pinch flats. If you are pinch flatting Big Apples, put more air in, they will still be cushy. The pressure required depends on the mass of the rider.